Related Topics: More Lessons for Grade 4 Free Math Worksheets
Videos, examples, solutions, and stories to help Grade 4 students learn the Divisibility Rules for 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13.
The following table gives the Divisibility Rules for 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12. Scroll down the page for examples and solutions. Divisibility Tests for 2, 3, 5, 7 and 11 This shows you the divisibility tests for 2, 3, 5, 7, and 11, so you can tell if those numbers are factors of a given number or not without dividing. Divisibility Test for 2: The last digit is 0, 2, 4, 6, or 8. Divisibility Test for 3: The sum of the digits is divisible by 3. Divisibility Test for 5: The last digit is 0 or 5. Divisibility Test for 7: Cross off last digit, double it and subtract. Repeat if you want. If new number is divisible by 7, the original number is divisible by 7. Divisibility Test for 11: For a 3digit number, sum of the outside digits minus the middle digit must be 0 or 11.
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Divisibility Tests for 11 and 13 Goes over two divisibility tests for 11 and also the one for 13.
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Divisibility Rules for 2, 3, 4, 5, 6, 8, 9, 10, and 12 Learn the divisibility rules for 2,3,4,5,6,8,9,10, and 12. Divisibility – One number divides into another number and there is nor a remainder.
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Divisibility Rule of Six A number is divisible by 6, if it is divisible by both 2 and 3.
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Divisibility Rule of ten A number is divisible by 10 if it ends in a zero.
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Divisibility Rules – 4, 5, 8, 10  sofatutor.com
Billy Bonka is bonkers for making sweet treats.
Customers love his delicious candy concoctions and the latest batch is ready. Billy just needs to divide the batch into packages with 4, 5, 8 or 10 treats.
To figure this out, Billy Bonka can use the rules of divisibility.
In his latest batch, Billy made 1516 blueberry balls, 1035 caramel cubes, and 1600 strawberry strips and he has packaging for 4, 5, 8 and 10 treats per package.
Billy wants to package the treats without having any remainders, so he must divide the number of treats among the packages evenly. Okay, let’s get to work.
Which of the candies can Billy pack into packs of 5?
Divisibility by 5
First, let's list the mutiples of 5.
5, 10, 15, 20, 25, 30 and so on. What do the multiples all have in common? They all end in a 5 or a 0.
So, for a number to be divisible by 5, it must end in a 5 or a 0.
The number 1516 doesn’t end in a 5 or a zero. So, we can safely tell Billy that 1516 isn't evenly divisible by 5.
As for the last two numbers, 1035 and 1600, one ends in a 5 and one ends in a 0, so both numbers must be divisible by 5.
Divisibility by 10
But what if Billy wants to divide the candies into packages of 10? He could figure this out using long division, but there's a faster way to determine if a number is divisible by 10.
Because every multiple of 10 ends with a 0a number is divisible by 10 if it also ends with a 0. The number of blueberry balls doesn’t end with a 0, so this number is not divisible by 10.
Divisibility by 4
Maybe Billy can pack the candies into groups of 4? There's a special rule you can use when deciding whether or not a number is divisible by 4, just concentrate on the last two digits! That's right! No matter how long a number is, if the last two digits are divisible by 4, then the whole number is divisible by 4 as well.
Let’s try this out. The last two digits of the number 1516 are 16 and since 16 is evenly divisible by 4, 1516 should be divisible by 4 as well.
To check, we can perform long division. 4 goes into 15 three times, bring down the one. 4 goes into 31 seven times, subtract 28 from 31and finally, bring down the 6.
Would ya look at that?! 1516 IS divisible by 4!
But why does this work? When dividing by 4, you're really just dividing by 2 twice!
Divide by two and then by two again.
If the quotient is a whole number, then the dividend is divisible by 4.
For 1035, the last two digits are 35.
Is 35 evenly divisible by 4?
Finally, if the last two digits of the number in question are both 0, then the number is divisible by 4! Pretty easy, right?
Divisibility by 8
But what about packs of 8?
Although the rule for 8 might seem a little tricky, it can save you a lot of time.
For multiples of 8, if the last three digits are divisible by 8, then the entire number is divisible by 8.
Is 516 divisible by 8? 8 goes into 51 six times, bring down the 6 and since 8 doesn't go into 36 an even number of times, 516 isn't evenly divisible by 8 and therefore neither is 1516.
Using the Divisibility Rules
What can Billy do with the 1035 cubes of chewy caramels? Let’s use the divisibility
Divisibility Rules
We say that a number is divisible if it can be divided evenly with no reminder.
2
If the last digit is even – 0, 2, 4, 6 or 8.
Example
258 is divisible by 2 because the last digit is 8.
170 is divisible by 2 because the last digit is 0.
3
If the sum of the digits is divisible by 3.
Example
246 is divisible by 3 because 2 + 4 + 6 = 12 – divisible by 3 (12 = 3 × 4).
954 is divisible by 3 because 9 + 5 + 4 = 18 – divisible by 3 (18 = 3 × 6).
4
If the last two digits form a number that is divisible by 4.
Example
316 is divisible by 4 because 16 is divisible by 4 (16 = 4 × 4).
528 is divisible by 4 because 28 is divisible by 4 (28 = 4 × 7).
5
If the last digit is 5 or 0.
Example
135 is divisible by 5 because the last digit is 5.
770 is divisible by 5 because the last digit is 0.
6
If the number is divisible by both 2 and 3.
Example
282 is divisible by 6 becuase it is divisible by 2(the last digit is even) and divisible by 3 (2+8+2 = 3 × 4).
780 is divisible by 6 becuase it is divisible by 2(the last digit is even) and divisible by 3 (7+8+0 = 3 × 5).
7
If you can double the last digit and subtract the sum from the rest of the number, and get an answer that is divisible by 7(including 0).
Example
203 is divisible by 7 because 20 – 2 ⋅ 3 = 14 – divisible by 7 (2 × 7 = 14).
455 is divisible by 7 because 45 – 2 ⋅ 5 = 35 – divisible by 7 (5 × 7 = 35).
8
If the last three digits form a number that is divisible by 8.
Example
1888 is divisible by 8 because 888 = 8 × 111.
1112 is divisible by 8 because 112 = 8 × 14.
9
If the sum of all digits is divisible by 9.
Example
144 is divisible by 9 because 1 + 4 + 4 = 9 and 9 is divisible by 9.
819 is divisible by 9 because 8 + 1 + 9 = 18 and 18 is divisible by 9.
10
If the number ends in 0.
Example
990 is divisible by 10 because it ends in 0.
2340 is divisible by 10 because it ends in 0.
Problems involving divisibility rules for 2, 3, 4, 5, 6, 9
Divisibility Rules Quiz – 1
Divisibility Rules Quiz – 2
Quiz: LCM and Divisibility Rules
Articles:
Divisibility
Divisibility by 2
Divisibility by 4
Divisibility by 3 and 9
Divisibility by 5
Divisibility by 25
Divisibility Rules and Tests
Worksheet on Divisibility Rules
There are many shortcuts or tricks that allow you to test whether a number, or dividend, is divisible by a given divisor.
This page focuses on the mostfrequently studied divisibility rules which involve divisibility by
2,
3,
4,
5,
6,
8,
9,
10, and
by 11

Rules:
 divisible by 2
 by 3
 by 4
 by 5
 by 6
 by 8
 by 9
 by 10
 by 11
Answer:
Almost everyone is familiar with this rule, which states that any even number can be divided by 2.
Even numbers are multiples of 2. A number is even if it ends in 0, 2, 4, 6, or 8.
Examples of numbers that are even and therefore pass this divisibility test.
Number  Explanation 
12  Since the last digit is a 2, the entire number, 12, is an even numberand therefore divisible by 2. 
318  Since the last digit is an 8, this is an an even number and therefore divisible by 2. 
310  Since the last digit is 0, this is an an even number and therefore divisible by 2. 
32,814  Since the last digit is a 4, this is an even number and therefore divisible by 2. 
Check if any number is divisible by two. Type in any number that you want, and the calculator will use the rule for divisibility by 2 to explain the result.
See what the rule for divisibility by two has to say about the following number:
Examples of numbers that are do not pass this divisibility test because they are not even.
Number  Explanation 
3  3 is not an even number. 
103  Not an even number. 
157  Not an even number. 
221  Not an even number. 
Practice Quiz on divisibility by 2

Rules:
 divisible by 2
 by 3
 by 4
 by 5
 by 6
 by 8
 by 9
 by 10
 by 11
Answer:
Rule: A number is divisible by 3 if the sum of its digits is divisible by 3.
375, for instance, is divisible by 3 since sum of its digits (3+7+5) is 15. And 15 is divisible by 3.
Number  Explanation 
12  $$ 1 + 2 = 3$$ and 3 is divisible by 3. 
36  $$ 3 + 6 = 9 $$ and 9 is divisible by 3. 
102  $$1 + 0 + 2 = 3$$ and 3 is divisible by 3. 
100,002,000  $$ 100,002,000 = 1 + 0 + 0 + 0 + 0 + 2 + 0 + 0 + 0 = 3$$ and 3 is divisible by 3. 
36  $$ 3 + 6 = 9 $$ and 9 is divisible by 3. 
Examples of numbers that do not pass this test:
Number  Explanation 
14  1 + 4 = 5 and since 5 is not divisible by 3, so 14 is also not. 
124  $$1 + 2 + 4 = 7$$ which is no good, since 7 is not evenly divisible by 3. 
100,002,001  $$1 + 0 + 0 + 0 + 2 + 0 + 0 + 1 = 4$$ so this very large also does not pass this divisibility test. 
Practice Quiz on divisibility by 3

Rules:
 divisible by 2
 by 3
 by 4
 by 5
 by 6
 by 8
 by 9
 by 10
 by 11
Answer:
Rule: A number is divisible by 4 if the number's last two digits are divisible by 4.
9,312, for instance, is divisible by 4 since its last 2 digits are 12. And 12 is divisible by 4.
Examples of numbers that are divisible by 4:
Number  Explanation 
112  Since the last two digits, 12, are divisible by 4, the number 112 is also divisible by 4. 
10,948  The last two digits, 48, are divisible by 4. Therefore, the whole number is also. 
100,002,088  Yep, this satisfies rule because 88 is divisible by 4! 
12,036  36 and 36 is evenly divided by 4, so 12,036 passes the test! 
Examples of numbers that are do not pass this divisibility test.
Number  Explanation 
113  Since the last two digits, 13, are not divisible by 4, the whole number does not pass this divisibility test. 
10,941  The last two digits, 41, are not de visible by 4. Therefore, the whole number does not satisfy the rule for 4. 
100,002,014  Those last two digits, 14, do not work. 
1,011  11 is not divisible by 4, so 1,011 fails this test. 
Ever wonder why these rules work. The test for 4 makes sense if you just break down the numbers. Think about what this rule says: “All that matters is whether or not the last two digits are divisible by 4.” Let's look at why this rule is true.
Examine some three digit numbers

124 is the same as 100 + 24, and we know that 100 is divisible by 4 so all that matters here is whether or not 24, or the last two digits, are divisible by 4. The same could be said for any three digit number 224 = 200 + 24, and we know that 200 is divisible by 4 so again all that we're worried about are these last two digits.
 Any multiple of 100 is divisible by four! Whether you're talking about 300, 700, 1000, 1100, 123,000 — All of these multiples of 100 are divisible by 4, which means that all that we ever have to worry about is the last two digits!

Rules:
 divisible by 2
 by 3
 by 4
 by 5
 by 6
 by 8
 by 9
 by 10
 by 11
Practice Quiz on divisibility by 4
Answer:
Rule: A number is divisible by 5 if its last digit is a 0 or 5.
Examples of numbers that are divisible by 5 and satisfy this rule
Number  Explanation 
10  Since the last digit is 0, this number is divisible by 5. 
15  Since the last digit is 5, this number is divisible by 5. 
45  Since the last digit is 5, this number is divisible by 5. 
Examples of numbers that are not divisible by 5.
Number  Explanation 
11  To be divisible by 5, the last digit must be 0 or 5. So 11 fails this test. 
19  To be divisible by 5, the last digit must be 0 or 5. So 19 fails this test. 

Rules:
 divisible by 2
 by 3
 by 4
 by 5
 by 6
 by 8
 by 9
 by 10
 by 11
Practice Quiz on divisibility by 5
Answer:
 Since 6 is a multiple of 2 and 3, the rules for divisibility by 6 are a combination of the rule for 2 and the rule for 3.
 In other words, a number passes this divisibility test only if it passes the testfor 2 and the for 3.
 Rule: A number is divisible by 6 if it is even and if the sum of its digits is divisible by 3.
Examples of numbers that are divisible by 6.
Number  Explanation 
114 
Therefore, 114 is divisible by 2 and by 3 ..so, yes , 114 is divisible by 6. 
241,122 
Therefore, 241,122 is divisible by 2 and by 3 ..so, yes, 241,122 is divisible by 6. 
Examples of numbers that are do not pass this divisibility test.
Number  Explanation 
207 
So, no, 204 is not divisible by 6. 
241,124 
So, no, 204 is not divisible by 6. 

Rules:
 divisible by 2
 by 3
 by 4
 by 5
 by 6
 by 8
 by 9
 by 10
 by 11
Practice Quiz on divisibility by 6
Rule A number passes the test for 8 if the last three digits form a number is divisible 8.
Examples of numbers that satisfy this rule and are divisible by 8.
Number  Explanation 
9,640  The last 3 digits, 640, are divisible by 8. Therefore, 9,640 is divisible 8 as well! 
77,184  The last 3 digits , 184, are divisible by 8. Therefore, 77,184 is divisible 8 as well! 
20,233,322,496  The last 3 digits, 496, are divisible by 8. Therefore , 20,233,322,496 is divisible 8 as well! 
Examples of numbers that are do not pass this divisibility test.
Number  Explanation 
9,801  Since last 3 digits are not divisible by 8, the entire number 9,801 is not. 
32,344,588  Since last 3 digits are not divisible by 8, the entire number 32,344,588 is not. 

Rules:
 divisible by 2
 by 3
 by 4
 by 5
 by 6
 by 8
 by 9
 by 10
 by 11
Practice Quiz on divisibility by 8
Rule A number is divisible by 9 if the sum of the digits are evenly divisible by 9.
Examples of numbers that satisfy this rule and are divisible by 9.
Number  Explanation 
4,518  $$ 4 + 5 + 1 + 8 = 18$$ which is divisible by 9, so 4,518 is divisible by 9. 
6,993  $$ 6 + 9 + 9 + 3 = 27 $$ which is divisible by 9 so, the entire number is divisible by 9. 
Examples of numbers that are do not pass this divisibility test.
Number  Explanation 
6,992  $$ 6 + 9 + 9 + 2 = 26 $$ which is not divisible by 9 so, the entire number is not divisible by 9. 
4,517  $$ 4 + 5 + 1 + 7 = 17$$ which is not divisible by 9 so, the entire number is not divisible by 9. 

Rules:
 divisible by 2
 by 3
 by 4
 by 5
 by 6
 by 8
 by 9
 by 10
 by 11
Practice Quiz on divisibility by 9
Rule A number passes the test for 10 if its final digit is 0
Use the divisibility calculator below to determine if any number is divisible by ten. Type in any number that you want, and the calculator will use the rule for divisibility by 10 to explain the result.
Examples of numbers that are divisible by 10.
Number  Explanation 
190  Last digit is 0, that's all that is needed for a number to be divisible by 10. 
231,110  Last digit is 0, that's all that is needed for a number to be divisible by 10. 
Examples of numbers that do not pass this divisibility test
Number  Explanation 
31,205  Since the last digit is not 0, this number is not divisible by 10. 
100,002  Since the last digit is not 0, this number is not divisible by 10. 

Rules:
 divisible by 2
 by 3
 by 4
 by 5
 by 6
 by 8
 by 9
 by 10
 by 11
Practice Quiz on divisibility by 10
Rule A number passes the test for 11 if the difference of the sums of alternating digits is divisible by 11.(This abstract and confusing sounding rule is much clearer with a few examples).
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