Is 7,866 divisible by 2, 3, 4, 6 and 9

Step by step

The question

Question: is 7866 divisible by 2, 3, 4, 6 and 9?

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

1 Look at the last digit

7866 is 786 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 Look at the last two digits

100 is 4 times 25.

So 4 goes into every hundred.

Only the last two digits are left: 66.

66 divided by 4 is 16, with 2 left over.

So no.

Careful!

Even is not enough for 4.

7866 is even, but 4 does not go into 66.

3 Add the digits

We add the digits: 7 + 8 + 6 + 6 is 27.

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: 27 divided by 3 is 9, nothing left over.

So 3 goes into 7866.

For 9: 27 divided by 9 is 3, nothing left over.

So 9 goes into 7866.

4 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.

5 Write the answer

So 7866 is divisible by 2, 3, 6 and 9.

Not by 4.

6 Check

Let's check by dividing.

7866 divided by 2 is 3933, nothing left over.

Every yes divides exactly, and 4 leaves 2 over.

The tests were right!

Let's look back.

First: look at the last digit.

Then: look at the last two digits.

Then: add the digits.

Then: use 2 and 3.

Then: write the answer.

Last: check.