How to Explain Patterns in Division

Divisibility Rules for Divisors 2 Though 5

• 1

  Explain that every division problem has two parts: a dividend and a divisor. A dividend is usually the biggest number, and it is the number that is being split into pieces. The divisor is the number that is splitting the dividend into pieces. For example, in the problem 584/2, 584 is the dividend and 2 is the divisor. Explain that by looking at the divisor and certain parts of the dividend, you can easily identify whether a number can be divided evenly or not.

• 2

  Look at the last digit in the number (the number furthest to the right). If it is even, then the number is divisible by 2.

  Example: The last digit in the number 536 is 6 which is an even number, so 536 is divisible by 2. 536 divided by 2 is 268.

• 3

  Add up all of the digits in the number. If the sum of the digits can be divided by 3 evenly, then the whole number is divisible by 3.

  Example: In the number 813, the digits 8+3+1 = 12. 12 is divisible by 3, so 813 is divisible by 3. 813 divided by 3 is 271.

• 4

  Look at the last two digits of the number. If those two digits can be divided by 4, then the whole number is divisible by 4.

  Example: The last two digits of 516 form the number 16. 16 can be divided by 4, so 516 is divisible by 4. 516 divided by 4 is 129.

• 5

  Look at the last digit in the number. If the last digit is a 0 or a 5, then the number is divisible by 5.

  Example: 5 is the last digit in 4,245, so it is divisible by 5. 4245 divided by 5 is 849.

Divisibitlity Rules for Divisors 6, 9 and 10

• 6

  Apply the rules for divisors 2 and 3 to the number. If both of these rules work, then the number is divisible by 6.

  Example: With the number 336, you can see that 6 is even, so you know that it can be divided by 2. You can then apply the rule for a divisor of 3 by adding up 3+3+6 = 12. 12 is divisible by 3, so the rule for 3 works as well. Both the rules for the divisors 2 and 3 work, so we know that 336 is divisible by 6. 336 divided by 6 is 56.

• 7

  Add up the digits of the number. If the sum is divisible by 9, then the whole number is divisible by 9.

  Example: In the number 594, the digits 5+9+4 add up to 18. 18 is divisible by 9, so 594 is divisible by 9. 594 divided by 9 is 66.

• 8

  Look at the last digit in the number. If it is a 0, then the whole number is divisible by 10.

  Example: The last digit in 1,450 is 0, so the number is divisible by 10. 1,450 divided by 10 is 145.