Step by step
The question
Question: is 5625 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
5625 is 562 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: 25.
25 divided by 4 is 6, with 1 left over.
So no.
3 Add the digits
We add the digits: 5 + 6 + 2 + 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 5625.
Careful!
For 3, the last digit does not tell us.
5625 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 5625.
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 5625 is divisible by 3, 5 and 9.
Not by 2, 4, 6 or 10.
6 Check
Let's check by dividing.
5625 divided by 3 is 1875, 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.