Divisibility Rules

The ability to be evenly divided. There will be no remainder. Divisible The ability to be evenly divided. There will be no remainder.

Example: 15 is divisible by 3 because you can divide those 2 numbers evenly without a remainder.

help you decide if a number is a factor of another number. Divisibility Rules help you decide if a number is a factor of another number.

Divisibility Rules Is 4 a factor of 64? We can use the divisibility rules to help us decide!

A number is evenly divisible by 2 if it is even. Two: A number is evenly divisible by 2 if it is even. Even numbers end in 0, 2, 4, 6, and 8.

Decide if the following numbers are divisible by two. (even numbers) Decide if the following numbers are divisible by two. Yes! 98 56 Yes! No! 17 87 No! No! 105 Yes! 38

45 is divisible by 3 because… Three: A number is evenly divisible by 3 if the sum of all the digits is a multiple of 3. Example: 45 is divisible by 3 because… 4 + 5 = 9 and 9 is a multiple of 3!

912 63 51 47 103 94 Three: Yes! Yes! Yes! No! No! No! (sum of all digits is a multiple of 3) Decide if the following numbers are divisible by three. Yes! 912 63 Yes! Yes! 51 47 No! No! 103 No! 94

Four: A number is evenly divisible by 4 if the number formed by the last two digits are divisible by 4. Example: 312 is divisible by 4 because… The last two digits are 12 and 12 is divisible by 4!

Four: (last two digits are a multiple of 4) Decide if the following numbers are divisible by four. 114 No! 912 Yes! 332 Yes! 911 No! 524 Yes!

Five: A number is evenly divisible by 5 if it ends in a 5 or a 0. Example: 930 is divisible by 5 because… It ends in a zero!

Decide if the following numbers are divisible by five. (ends in a 5 or 0) Decide if the following numbers are divisible by five. 65 90 58 Yes! Yes! No! 105 42 650 No! Yes! Yes!

Six: A number is evenly divisible by 6 if it is divisible by both 2 and 3! Follow the rules for BOTH!  Example: 84 is divisible by 6 because… It is even AND is divisible by 3 because 8 + 4 = 12 and 12 is a multiple of 3!

Decide if the following numbers are divisible by six. (follows rules of 2 and 3) Decide if the following numbers are divisible by six. 924 138 90 Yes! Yes! Yes! 34 63 No! 72 No! Yes!

891 is divisible by 9 because… Nine: A number is evenly divisible by 9 if the sum of the digits is a multiple of 9! Example: 891 is divisible by 9 because… 8 + 9 + 1 = 18 and 18 is a multiple of 9!

612 27 71 53 441 81 Nine: No! Yes! Yes! No! Yes! Yes! Sum of all digits is a multiple of 9 Decide if the following numbers are divisible by nine. 612 27 71 No! Yes! Yes! 53 No! 441 81 Yes! Yes!

Ten: Example: A number is evenly divisible by 10 if it ends in a zero! 870 is divisible by 10 because it ends in a zero!

Decide if the following numbers are divisible by ten. Ends in a zero Decide if the following numbers are divisible by ten. 40 604 31 No! Yes! No! 320 880 41 No! Yes! Yes!