As your kids develop their mathematical skills, the will start to discover the rules that guide computation and problem solving. Rules in math are based on patterns. Students learn to recognize these patterns in different math situations as well as the rules connected to these pattern.
Today, we are going to take a look at divisibility rules.
What are divisibility rules?
Divisibility rules are a quick way of working out if a number is divisible by a fixed number without performing the division. This is usually done by examining that number’s digits. The best way to explain this is to jump right in. We are going to show you the divisibility rules for the fixed numbers 1 to 9.
Divisibility by 1
This one is easy: every number is divisible by 1.
Divisibility by 2
The number should have 0, 2, 4, 6, or 8 as the unit’s digit. For example:
The unit digit is 0 so 1,240 is divisible by 2.
Divisibility by 3
If the sum of the digits is divisible by 3, the number is divisible by 3. For example:
The sum of the digits is 12. 12 divided by 3 is 4, so 381 is divisible by 3.
Divisibility by 4
If the numbers in the tens and units places is divisible by 4, the number is divisible by 4. For example:
12 divided by 4 is 3. 1312 is divisible by 4.
Divisibility by 5
If a number has 0 or 5 in its unit place, that number is divisible by 5. For example:
Divisibility by 6
If a number is even and can be divided by 3, that number is divisible by 6. For example:
114 is an even number. In the divisibility 3 rule, the sum of the three digits is 6. 6 divided by 3 is 2. 114 is divisible by 6.
Divisibility by 7
If you double the unit digit and subtract it from the number made by the other digits, the resulting number must be divisible by 7. For example:
The double of 2 is 4. The number made by the other digits is 67. We subtract 4 from 67, which is 63. 63 divided by 7 makes 9. 672 is divisible by 7.
Divisibility by 8
The easiest way to check if a number is divisible by 8, you take the last three digits of that number. You then halve that number three times and when the result is still a whole number, the original number is divisible by 8. For example:
The last three digits of 110,816 is 816. 816 divided by 2 is 408. 408 divided by 2 is 204. 204 divided by 2 is 102. SO, 110,816 is divisible by 8.
Divisibility by 9
If the sum of the digits in a number is divisible by 9, that number is divisible by 9. For example:
By adding the digits of 1,629: 1 + 6 + 2 + 9, the sum is 18. 18 divided by 9 is 2. 1,629 is divisible by 9.
If you are looking for some mental division worksheets, you can find them in our grade 4 division section.
