Divisibility Rules: A Quick Guide for Kids
Understanding divisibility rules can make math easier and more fun! These rules help you quickly figure out if a number can be divided evenly by another without having to do a lot of calculations. Let’s explore the most common divisibility rules:
Divisibility Rule for 2
A number is divisible by 2 if it ends in 0, 2, 4, 6, or 8. In other words, if it’s an even number, it can be divided by 2.
Example:
- 24 ends in 4, so it’s divisible by 2.
- 37 ends in 7, so it’s not divisible by 2.
When a number ends in one of these digits, it means it’s in a group that can be split into two equal parts.
Divisibility Rule for 3
Add up all the digits of the number. If the sum is divisible by 3, then the original number is also divisible by 3.
Example:
- For 123, add 1 + 2 + 3 = 6. Since 6 is divisible by 3, 123 is also divisible by 3.
- For 85, add 8 + 5 = 13. Since 13 is not divisible by 3, 85 is not divisible by 3.
If the sum of digits of a number can evenly divide by 3, then the original number can also be divided by 3. If 243 is divisible by 3, other numbers like 234, 324, 342, 423 and 432 formed using the same digits can also be divided by 3. This is because the rule for divisibility by 3 depends on the sum of the digits, not the order of the digits.
Divisibility Rule for 4
A number is divisible by 4 if the last two digits form a number that is divisible by 4.
Example:
- In 132, the last two digits are 32. Since 32 is divisible by 4, 132 is also divisible by 4.
- In 127, the last two digits are 27, which is not divisible by 4, so 127 is not divisible by 4.
The last two digits tell us about the number in groups of 100. Since each group of 100 can be divided into 4 smaller groups, checking the last two digits helps us see if the whole number can be divided by 4.
Divisibility Rule for 5
If a number ends in 0 or 5, it is divisible by 5.
Example:
- 40 ends in 0, so it’s divisible by 5.
- 23 does not end in 0 or 5, so it’s not divisible by 5.
0 and 5 are always the last digits of numbers that fit perfectly into groups of 5.
Divisibility Rule for 6
A number is divisible by 6 if it is divisible by both 2 and 3.
Example:
- 72 is even (divisible by 2) and the sum of its digits (7 + 2 = 9) is divisible by 3. So, 72 is divisible by 6.
- 55 is not even, so it’s not divisible by 6.
- 88 is even (divisible by 2), but the sum of its digits (8 + 8 = 16) is not divisible by 3. So, 88 is not divisible by 6.
If a number can be divided by both 2 and 3, it can also be divided by 6. This is because 6 is made up of both 2 and 3.
Divisibility Rule for 8
A number is divisible by 8 if the last three digits form a number that is divisible by 8.
Example:
- In 5,624, the last three digits are 624. Since 624 ÷ 8 = 78 (a whole number), 5,624 is divisible by 8.
- In 3,245, the last three digits are 245, which is not divisible by 8, so 3,245 is not divisible by 8.
The last three digits of a number tell us how the number fits into groups of 1000. Since 1000 can be divided into smaller groups of 8, checking just the last three digits helps us see if the whole number can also be split into groups of 8.
Divisibility Rule for 9
Add up all the digits of the number. If the sum is divisible by 9, then the original number is also divisible by 9.
Example:
- For 729, add 7 + 2 + 9 = 18. Since 18 is divisible by 9, 729 is also divisible by 9.
- For 45, add 4 + 5 = 9. Since 9 is divisible by 9, 45 is divisible by 9.
Divisibility Rule for 10
A number is divisible by 10 if it ends in 0.
Example:
- 80 ends in 0, so it’s divisible by 10.
- 83 does not end in 0, so it’s not divisible by 10.
Numbers ending in 0 can always be split into groups of 10 without any remainders.
Divisibility Rule for 11
A number is divisible by 11 if the difference between the sum of its digits in odd positions and the sum of its digits in even positions is 0 or divisible by 11.
Example:
- For 1,210, (1 + 0) – (2 + 1) = 1 – 3 = -2 (not divisible by 11), so 1,210 is not divisible by 11.
- For 2,640, (2 + 4) – (6 + 0) = 6 – 6 = 0, so 2,640 is divisible by 11.
Practice Quiz on Divisibility Rules
FAQs on Divisibility Rules
- A number is divisible by 12 if it is divisible by both 3 and 4.
- Yes, divisibility rules apply to negative numbers just as they do for positive numbers. The sign does not affect divisibility.
- No, divisibility rules apply only to whole numbers (integers).
Yes, but they become more complex. For instance:
- Divisibility by 13: Remove the last digit, multiply it by 9, and subtract it from the remaining number. Repeat if necessary.
- Divisibility by 17: Remove the last digit, multiply it by 5, and subtract it from the remaining number.
- Yes, divisibility rules are helpful for quickly identifying common factors, which can be used to simplify fractions.
- They allow you to quickly identify which prime numbers divide a given number, speeding up the factorization process.
- No, there isn’t a simple, universally known rule for all prime numbers like 13, 17, or larger primes. However, specific techniques exist for some primes, though they may not be straightforward.
- Any number is divisible by 1, so the rule is trivial and doesn’t require a specific test.