Divisibility TestsDivisibility Tests

Is 24672312 divisible by 3?Is 24672312 divisible by 3?

An integer is divisible by 2 if…An integer is divisible by 2 if…

. . .it ends in an even digit.. . .it ends in an even digit.

So 345,678,234,624 is divisible by 2. I can’t even

say that number!

An integer is divisible by 3 if . . .An integer is divisible by 3 if . . .

. . .the sum of the digits is a multiple of 3.. . .the sum of the digits is a multiple of 3.

So 24,672,312 is divisible by 3 because 2 + 4 + 6 + 7 + 2 + 3 + 1 + 2 equals

27 which is a multiple of 3. Wow that’s amazing!

An integer is divisible by 4 if . . .An integer is divisible by 4 if . . .

. . .the number formed by the final two . . .the number formed by the final two digits is divisible by 4.digits is divisible by 4.

So 976,816 is divisible by 4 because 16 is divisible by

4!

An integer is divisible by 5 if . . .An integer is divisible by 5 if . . .

. . .the final digit is 0 or 5.. . .the final digit is 0 or 5.

So 9,756,439,275,975 is divisible by 5.

What a big number!

An integer is divisible by 6 if . . .An integer is divisible by 6 if . . .

. . .the final digit is even and the digit sum . . .the final digit is even and the digit sum is divisible by 3.is divisible by 3.

So 78,642 is divisible by 6 because 7 + 8 + 6 + 4 + 2 = 27 AND it’s an even number!

An integer is divisible by 8 if . . .An integer is divisible by 8 if . . .

. . .the number formed by the final 3 digits . . .the number formed by the final 3 digits is divisible by 8.is divisible by 8.

So 458,112 is divisible by 8

because 112 is divisible by 8.

That’s a bit hard to do!

An integer is divisible by 9 if . . .An integer is divisible by 9 if . . .

. . .the sum of the digits is divisible by 9.. . .the sum of the digits is divisible by 9.

So 362,178 is divisible by 9 because 3 + 6 + 2 + 1 + 7 + 8 = 27 which

is a multiple of 9!I’m getting the hang of

this now!

An integer is divisible by 10 if . . .An integer is divisible by 10 if . . .

. . .the final digit is 0.. . .the final digit is 0.

So it’s easy to tell if a number is

divisible by 10!

An integer is divisible by 11 if . . .An integer is divisible by 11 if . . .

. . .the difference between the sums of . . .the difference between the sums of alternating digits is divisible by 11.alternating digits is divisible by 11.

So 72,479 is divisible by 11 because

(7 + 4 + 9) – (2 + 7) = 11 and 11 is divisible by 11.

I never knew that!