1.5 Divisibility Rules

SRB pg 11.

Rule for 2:

All even numbers (0, 2, 4, 6, & 8) are divisible by two.

Is 1,098 divisible by 2? Yes, it’s an even number.

Is 23,589 divisible by 2? No, it’s an odd number.

Is 998,876 divisible by 2? Yes, it’s an even number.

Rule for 3

A number is divisible by 3 if the sum of its digits is divisible by 3.

Ex. 2,301 is divisible by 3 because:2+3+0+1=6 and 6÷3=2

Is 5,890 divisible by 3? No 5+8+9+0 = 22; 22 can not be evenly divided

by 3. (22÷3=7 r1) Is 45,369 divisible by 3?

Yes 4+5+3+6+9= 27; 27÷3=9

Rule for 5

Any number that ends in 0 or 5 is divisible by 5.

Is 256 divisible by 5? No, it ends in 6.

Is 36,650 divisible by 5? Yes, it ends in 0.

Is 5,895 divisible by 5? Yes, it ends in 5.

Rule for 6

A number is divisible by 6 if it is divisible by 2 and 3.

Ex. 384 is divisible by 6 because it is even (ends in 4) and 3+8+4=15; 15÷3=5.

Is 75 divisible by 6? No, it is an odd number.

Is 82 divisible by 6? No, 8+2=10, and 10 ÷ 3 = 3 r1

Is 96 divisible by 6? Yes, it is even and 9+6=15; 15÷3=5

Rule for 9

A number is divisible by 9 if the sum of its digits are divisible by 9.

Ex. 3,726 is divisible by 9 because 3+7+2+6=18; 18÷9=2

Is 7,960 divisible by 9? No 7+9+6+0=22; 22÷9= 2 r4

Is 9,819 divisible by 9? Yes, 9+8+1+9=27; 27÷9=3

Rule for 10

Any number that ends in 0 is divisible by 10.

Is 45,256 divisible by 10? No, it ends in a 6.

Is 5,123,320 divisible by 10? Yes it, ends in 0.

Is 770 divisible by 10? Yes, it ends in 0.

Extra Practice

From our rules, which numbers is 36,540 divisible by?

It is divisible by 2, 3, 5, 6, 9, &10.From our rules, which numbers is 4,009,721 divisible by?

It is not divisible by any of the numbers.From our rules, which numbers is 5,890 divisible by?

It is divisible by 2, 5, & 10.