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Divisibility
Rules
2, 3, 4, 5, 6, 9, 10
“DIVISIBLE BY”
WHAT DOES IT MEAN?
“Divisible by” means:
If you divide one number by another, the result is a
whole number WITHOUT a remainder.
Examples:
12 ÷ 6 = 2 No remainder
15 ÷ 5 = 3 No remainder
DIVISIBILITY RULE 2
A number is divisible by 2 if the
last digit is even (0, 2, 4, 6, 8).
Examples:
78
3470
ARE THE FOLLOWING NUMBERS DIVISIBLE BY 2?

32
Yes, the number ends in a 2.

153
No, the number ends in a 3.

2386
Yes, the number ends in a 6.

59841
No, the number ends in a 1.

697157
No, the number ends in a 7.

7134784
Yes, the number ends in a 4.
DIVISIBILITY RULE 3
A number is divisible by three if the sum
of the digits is divisible by 3.
Examples:
75
7 + 5 = 12 12 ÷ 3 = 4 No Remainder
369 3 +6 + 9 = 18
18 ÷ 3 = 6 No Remainder
ARE THE FOLLOWING NUMBERS DIVISIBLE BY 3?

32
No, 3+2=5. 5 is not divisible by 3.

153
Yes. 1+5+3=9. 9 is divisible by 3.

2386
No, 2+3+8+6=19. 19 is not divisible by 3.

59841
Yes. 5+9+8+4+1=27. 27 is divisible by 3.

697157
No, 6+9+7+1+5+7=35. 35 is not divisible by 3.

7134784
No, 7+1+3+4+7+8+4=34. 34 is not divisible by 3.
DIVISIBILITY RULE 4
A number is divisible by 4 if the last two digits are
divisible by 4.
Examples:
1320 20 ÷ 4 = 5
672
72 ÷ 4 = 18
ARE THE FOLLOWING NUMBERS DIVISIBLE BY 4?

136
Yes, 36 is divisible by 4.

2958
No, 58 is not divisible by 4.

88413
No, 13 is not divisible by 4.

73208
Yes, 8 is divisible by 4.

9547146
No, 46 is not divisible by 4.

72841532
Yes, 32 is divisible by 4.
DIVISIBILITY RULE 5
A number is divisible by 5 if the last
digit is a 0 or 5.
Examples:
615
ends in a 5
1480
ends on a 0
ARE THE FOLLOWING NUMBERS DIVISIBLE BY 5?

30
Yes, the number ends in a 0.

155
Yes, the number ends in a 5.

2386
No, the number ends in a 6.

59841
No, the number ends in a 1.

697150
Yes, the number ends in a 0.

7134785
Yes, the number ends in a 5.
DIVISIBILITY RULE 6
A number is divisible by 6 when it is divisible by
2 AND 3.
Examples:
408 is divisible by 6 because it ends in an even
number (divisible by 2), and 4+0+8=12 (divisible
by 3).
ARE THE FOLLOWING NUMBERS DIVISIBLE BY 6?

32
No, the number ends in a 2 (divisible by 2), but 3+2=5
(not divisible by 3).

156
Yes, the number ends in a 6 (divisible by 2), and
1+5+6=12 (divisible by 3).

2388
Yes, the number ends in an 8 (divisible by 2), and
2+3+8+8=21 (divisible by 3).

59841
No, the number ends in a 1

697157
No, the number ends in a 7

7134786
Yes, the number ends in a 6 (divisible by 2), and
7+1+3+4+7+8+6=36 (divisible by 3).
DIVISIBILITY RULE 9
A number is divisible by 9 if the sum of the
digits is divisible by 9.
Examples:
963 9 + 6 + 3 = 18 18 ÷ 9 = 2
5445 5 + 4 + 4 + 5 =18 18 ÷ 9 =2
ARE THE FOLLOWING NUMBERS DIVISIBLE BY 9?

32
No, 3+2=5. 5 is not divisible by 9.

153
Yes, 1+5+3=9. 9 is divisible by 9.

2385
Yes, 2+3+8+5=18. 18 is divisible by 9.

59841
Yes, 5+9+8+4+1=27. 27 is divisible by 9.

697157
No, 6+9+7+1+5+7=35. 35 is not divisible by 9.

7134786
Yes, 7+1+3+4+7+8+6=. 36 is divisible by 9.
DIVISIBILITY RULE 10
A number is divisible by 10 if it ends in a
ZERO.
Example:
7630 ends in a zero
410
ends in a zero
ARE THE FOLLOWING NUMBERS DIVISIBLE BY 10?

30
Yes, the number ends in a 0.

153
No, the number ends in a 3.

2386
No, the number ends in a 6.

59840
Yes, the number ends in a 0.

697157
No, the number ends in a 7.

7134780
Yes, the number ends in a 0.
Questions?