Is 564 divisible by 4 6 or 9 and why?

Answer 1

By "Why" I guess you mean "what test can be used to find the divisibility" as opposed to "showing what multiple works".

Test of divisibility by

• 4

If last 2 digits divisible by 4, the whole number is divisible by 4.

564 → 64 which is divisible by 4 (64 = 4 x 16), so 564 is divisible by 4

(564 = 4 x 141)

• 6

6 = 2 x 3, so the number must pass both the divisibility tests for 2 & 3:

• 2

The number is even (the last digit is divisible by 2)

564 → 4 which is even (4 = 2 x 2), so 564 is divisible by 2

(564 = 2 x 282)

• 3

Add the digits together and if the resulting number is divisible by 3, so is the original number.

564 → 5 + 6 + 4 = 15 which is divisible by 3 (15 = 3 x 5), so 564 is divisible by 3

(564 = 3 x 188)

564 passes both tests, so it is divisible by 6 (564 = 6 x 94)

• 9

Add the digits together and if the resulting number is divisible by 9, so is the original number

564 → 5 + 6 + 4 = 15 which is not divisible by 9, so 564 is not divisible by 9

Thus 564 is divisible by 4 and 6, but not by 9.

In the tests for 3 and 9, if the result of the addition is more than 1 digit, the test can be reapplied to the result of the addition, so if the digits of sum are added together until a single digit remains, then

• if the digit is 3, 6 or 9, it is divisible by 3 and so the original number is divisible by 3
• if it is 9, then the original number is also divisible by 9.