Divisibility tests for 8,415

Step by step

The question

Question: is 8415 divisible by 2, 3, 4, 5, 6, 9 and 10?

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

1 Look at the last digit

8415 is 841 tens and 5.

2, 5 and 10 all go 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 5.

So no.

For 5: is it 0 or 5?

The last digit is 5.

So yes.

For 10: is it 0?

The last digit is 5.

So no.

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: 15.

15 divided by 4 is 3, with 3 left over.

So no.

3 Add the digits

We add the digits: 8 + 4 + 1 + 5 is 18.

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: 18 divided by 3 is 6, nothing left over.

So 3 goes into 8415.

Careful!

For 3, the last digit does not tell us.

8415 ends in 5, and 3 still goes in.

We add the digits.

For 9: 18 divided by 9 is 2, nothing left over.

So 9 goes into 8415.

4 Use 2 and 3

6 is 2 times 3.

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

2 does not.

So no.

5 Write the answer

So 8415 is divisible by 3, 5 and 9.

Not by 2, 4, 6 or 10.

6 Check

Let's check by dividing.

8415 divided by 3 is 2805, nothing left over.

Every yes divides exactly, and 2 leaves 1 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.