Download Divisibility Rules

Divisibility and Mental
Math
Vocabulary
A number is divisible by another number if it can be divided
into and result in a remainder of 0.
24 is divisible by 4, because 24 ÷ 4 = 6.
24 is not divisible by 5, because 24 ÷ 5 = 4.8 (or 4R4).
An even number ends with a 0, 2, 4, 6, or 8.
An odd number ends with a 1, 3, 5, 7, or 9.
Divisibility Rules
2 divides into all even numbers.
3 divides into a number if the sum of the
digits of that number is divisible by 3.
4 divides into numbers where the last two
digits are divisible by 4.
5 divides into numbers that end with a 5 or
0.
Divisibility Rules
(continued)
6 divides into a number if it is divisible by
both 2 and 3.
9 divides into a number if the sum of the
digits of that number is divisible by 9.
10 divides into numbers that end with 0.
Example: Test each number
for divisibility by 3.
216
2+1+6=9
9 is divisible by 3, so 216 is divisible by 3.
yes
437
4 + 3 + 7 = 14
14 is not divisible by 3, so 437 is not divisible by 3.
no
Example: Test the number
for divisibility by 2, 5, or 10.
454,320
2 works because the number is even.
5 works because the number ends with 0.
10 works because the number ends with 0.
Is the number
divisible by 9?
4 + 5 + 4 + 3 + 2 + 0 = 18.
18 is divisible by 9, so 454,320 is also
divisible by 9.
Example: Test the number
for divisibility by 4
216
16 ÷ 4 = 4
16 is divisible by 4, so 216 is divisible by 4.
yes
Example: Test the number
for divisibility by 6
2 works because the number is even.
210
yes
436
no
2+1+0=3
3 is divisible by 3, so 210 is divisible by 3.
Because 2 & 3 both work…… then 6
automatically works.
2 works because the number is even.
4 + 3 + 6 = 13
13 is not divisible by 3, so 436 is not divisible by 3.
Since 3 doesn’t work, then 6 can’t work.
Homework Time