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Divisibility Rules
Outcome A6 – Develop and apply
divisibility rules for 3, 4, 6, 9
Divisibility rule for 3
If you add the digits of a number divisible
by three the sum must be divisible by
three.
 Example:

→ 4 + 6 + 5 = 15
 15 → 1 + 5 = 6
6 ÷ 3 = 2
 Because 6 was divisible by three 465 is divisible by
three
 465
Divisibility rule for 4
If a number is divisible by 4 the last two
digits are divisible by 4.
 Example:

 1364
→ 64 ÷ 4 = 16
**remember this works because 100 is divisible by 4
(100 ÷ 4 = 25) that means 1300 is divisible by 4 so
we only need to worry about the last two digits.
Divisibility rule for 6

If a number is divisible by 6 it must be
divisible by both 2 and 3.
 Remember
a number is divisible by two if it is
even. See earlier notes for divisibility of 3.

Example:
→ is an even number so it is divisible by 2
 672 → 6 + 7 + 2 = 15 → 1 + 5 = 6 → 6 ÷ 3 = 2
 Because the number meets both rules it is divisible
by 6.
 672
Divisibility rule for 9

If you add the digits of a number divisible
by 9 then the sum of the numbers must be
divisible by 9.

Example:
→ 5 + 7 + 6 = 18 → 18 ÷ 9 = 2
 576 is divisible by 9
 576
Divisibility Questions.
1. Is 136 divisible by 3?
Explain why or why not.
2. Is 244 divisible by 4.
Explain why or why not.
3. Is 294 divisible by 6?
Explain why or why not.
4. Is 5652 divisible by 9?
Explain why or why not.
5. Fill in the missing digit so
the numbers are divisible
by 9.
a.
b.
c.
34__
59__45
__5004
6. Guess the number…
The number is odd and greater
than 200 but less than 401. The
number is divisible by 5 and 9.
7. Guess the number…
The number is less than 100 and
is divisible by 2, 5 and 8.
8. Guess the number…
The number is less than 172 but
greater than 90. The number is
divisible by 3, 5, and 9.
9. Create your own guess
the number question.
Divisibility Answers.
1. Is 136 divisible by 3?
Explain why or why not.
No, because 1+3+6 = 10 and 10 is not
divisible by 3. The divisibility rule for
three is that if we add all the digits, the
sum must be divisible by three.
2. Is 244 divisible by 4.
Explain why or why not.
Yes, because 44 ÷ 4 = 11. The
divisibility rule for 4 is that if the last
two digits are divisible by four then the
whole number is divisible by 4.
3. Is 294 divisible by 6?
Explain why or why not.
Yes, because it is even and 2+9+4 =
15 and 15 ÷ 3 = 5. That means 294
meets the divisibility rule for 2 and 3
and is therefore divisible by 6.
4. Is 5652 divisible by 9?
Explain why or why not.
Yes, because 5+6+5+2 = 18 and 18 is
divisible by 9. Since the sum of the
digits is divisible by 9 then the number
is divisible by 9.
5. Fill in the missing digit so
the numbers are divisible
by 9.
34__ = 342
b. 59__45 = 59445
__5004 = 95004 or 05004
a.
c.
6. Guess the number… The number is
odd and greater than 200 but less than
401. The number is divisible by 5 and 9.
If the number is divisible by 5 and odd the last digit must be a 5. the
three numbers must add up to a multiple of 9. Since the last digit is a 5
the first two digits must add up to 4 or 13. They can’t add up to 13
because the first digit must be either 2 or 3.
If the first digit is a 2 and the last digit is a 5 then the number must be
225 (2+2+5=9)
If the first digit is a 3 then it must be 3+1+5=9 so 315
So there are two answers 225 and 315
7. Guess the number… The
number is less than 100 and is
divisible by 2, 5 and 8.
Because the number is divisible by both 2 and 5 the
number must end in a zero (5 must have a last digit of 5
or 0 but 5 is not even so it is not divisible by 2) so the
number could be 10, 20, 30, 40, 50, 60, 70, 80, or 90
The number must also be divisible by 8 so it could be
either 40 or 80 as they are both multiples of 8.
8. Guess the number…The number is less than
172 but greater than 90. The number is divisible
by 3, 5, and 9.
We
know that all numbers that are divisible by 9 are also
divisible by 3 so we only have to worry about 9 and 5.
From the divisibility rule for 5 we know the number must end
in a 5 or 0. From the divisibility rule for 9 we know the sum of
the digits must be divisible by 9.
If we guess the last digit is 0 then the first digit or first two
digits must add to 9. 90 does not work because the number
must be greater than 90. and the greatest number we can go
to is 170 but 1+7+0 is only 8 so we do not have a factor of 9.
So the last number must be 5.
If the last number is 5 then the first digit or digits must add
together with 5 to equal 9. The first digit must be a 1.
So 1+___+5=9 the second digit must be a 3
135 is divisible by 3, 5, and 9.
9. Create your own guess
the number question.
Practice
No Calculators allowed!!
 Textbook page 31-33

 #1-8,
11-13, 15, 18, 19