Divisibility Rules

divisibility rules for middle school math

1. Divisibility Rules What are they? Mrs. Rodriguez Math 7 – Finley Middle School

2. Factor Numbers that go into another number evenly. Example: Factors of 24 : 1,2,3,4,6,8,12,24 Factors of 8 : 1,2,4,8 Factors of 100 : 1,2,4,5,10,20,25,50,100

3. Rules to check the divisibility of a number Divisibility rule of 2 Number ends in an even number 0,2,4,6,8 Divisibility rule of 3 Sum of all digits is divisible by 3 Example: 213=2+1+3=6 6 ÷3=2 3 is a factor of 213, so it is divisible by 3

4. Rules to check the divisibility of a number Divisibility rule of 4 If the last 2 digits are divisible by 4. Example : 232: 32  4 = 6 4 is a factor and this number is divisible by 4 1273: 73  4=13.25 4 is not a factor so this number is not divisible by 4 Divisibility rule of 5 If the last digit is a 5 or a 0, then the value is divisible by 5. Example : 1,256: 5 is not a factor so this number is not divisible by 5 58,320: 5 is a factor so this number is divisible by 5

5. More divisibility rules Divisibility rule for 6 If the number is divisible by both 2 and 3 Examples: 342 is even and 3+4+2=9, 9/3 = 3 so this is divisible by 6 Divisibility rule for 8 If the last 3 digits are divisible by 8 Examples: 1,232: 232 8= 29 8 is a factor so the number is divisible by 8

6. More divisibility rules Divisibility rule for 7 Take the last digit, double it, and subtract it from the rest of the number; if the answer is divisible by 7 (including 0), then the number is also divisible by 7. Examples : 357: 7 x 2 = 14, 35 – 14 = 21, 21 is divisible by 7, so , 357 is also divisible by 7

7. Even More divisibility rules Divisibility rule for 9 If the sum of the digits is divisible by 9 Ex. 531 , 5+3+1=9 so 531 is divisible by 9 Divisibility rule for 10 If the digit in the ones place is 0 Ex. 790 ends in 0 so it is divisible by 10