Is 2,346 divisible by 6 and 9

Step by step

The question

Question: is 2346 divisible by 6 and 9?

Divisible means it goes in exactly, with nothing left over.

1 Look at the last digit

2346 is 234 tens and 6.

2 goes into 10, so into every ten.

Only the last digit is left to check.

For 2: is it even: 0, 2, 4, 6 or 8?

The last digit is 6.

So yes.

2 Add the digits

We add the digits: 2 + 3 + 4 + 6 is 15.

Why add the digits?

Each ten is 9 and 1 more.

Each hundred is 99 and 1 more.

3 and 9 go into the 9s and 99s.

What is left over is the sum of the digits.

For 3: 15 divided by 3 is 5, nothing left over.

So 3 goes into 2346.

For 9: 15 divided by 9 is 1, with 6 left over.

So 9 does not go into 2346.

Careful!

For 9, the sum must divide by 9, not only by 3.

15 divides by 3, but not by 9.

3 Use 2 and 3

6 is 2 times 3.

So 6 goes in only when 2 and 3 both go in.

Both do.

So yes.

4 Write the answer

So 2346 is divisible by 6.

Not by 9.

5 Check

Let's check by dividing.

2346 divided by 6 is 391, nothing left over.

2346 divided by 9 is 260, with 6 left over.

The tests were right!

Let's look back.

First: look at the last digit.

Then: add the digits.

Then: use 2 and 3.

Then: write the answer.

Last: check.