Steply

Divisibility tests

Foundations · 21 problems, easy to harder

▶ Watch the first one solved

How we do it

  1. Look at the last digit
  2. Look at the last two digits
  3. Add the digits
  4. Use 2 and 3
  5. Write the answer
  6. Check

The steps for Is 1290 divisible by 2, 3, 4, 5, 6, 9 and 10. Every solution names its steps, so you always know what comes next.

Worked examples

Is 348 divisible by 2 Easy

The question

Question: is 348 divisible by 2?

Is 348 divisible by 2?

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

divisible: no remainder

1 Look at the last digit

= 348

348 is 34 tens and 8.

2 goes into 10, so into every ten.

Only the last digit is left to check.

34 tens + 8

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

The last digit is 8.

So yes.

= ÷ 2: last digit 0, 2, 4, 6, 8? 8 → yes ✓

2 Write the answer

So 348 is divisible by 2.

= yes: 348 ÷ 2 has no remainder

3 Check

Let's check by dividing.

348 divided by 2 is 174, nothing left over.

348 ÷ 2 = 174

The tests were right!

Let's look back.

First: look at the last digit.

Then: write the answer.

Last: check.

Answer
= yes: 348 ÷ 2 has no remainder

▶ Watch it solved

Is 2,736 divisible by 9 Medium

The question

Question: is 2736 divisible by 9?

Is 2736 divisible by 9?

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

divisible: no remainder

1 Add the digits

We add the digits: 2 + 7 + 3 + 6 is 18.

= 2 + 7 + 3 + 6 = 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.

10 = 9 + 1, 100 = 99 + 1

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

So 9 goes into 2736.

= ÷ 9: 18 ÷ 9 = 2 → yes ✓

2 Write the answer

So 2736 is divisible by 9.

= yes: 2736 ÷ 9 has no remainder

3 Check

Let's check by dividing.

2736 divided by 9 is 304, nothing left over.

2736 ÷ 9 = 304

The tests were right!

Let's look back.

First: add the digits.

Then: write the answer.

Last: check.

Answer
= yes: 2736 ÷ 9 has no remainder

▶ Watch it solved

Is 1290 divisible by 2, 3, 4, 5, 6, 9 and 10 Harder

The question

Question: is 1290 divisible by 2, 3, 4, 5, 6, 9 and 10?

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

Is 1290 divisible by 2, 3, 4, 5, 6, 9 and 10?

1 Look at the last digit

= 1290

1290 is 129 tens and 0.

2, 5 and 10 all go into 10, so into every ten.

Only the last digit is left to check.

129 tens + 0

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

The last digit is 0.

So yes.

= ÷ 2: last digit 0, 2, 4, 6, 8? 0 → yes ✓

For 5: is it 0 or 5?

The last digit is 0.

So yes.

= ÷ 5: last digit 0 or 5? 0 → yes ✓

For 10: is it 0?

The last digit is 0.

So yes.

= ÷ 10: last digit 0? 0 → yes ✓

2 Look at the last two digits

= 1290

100 is 4 times 25.

So 4 goes into every hundred.

Only the last two digits are left: 90.

12 hundreds + 90 (100 = 4 × 25)

90 divided by 4 is 22, with 2 left over.

So no.

= ÷ 4: 90 ÷ 4 = 22 r 2 → no ✗

Careful!

Even is not enough for 4.

1290 is even, but 4 does not go into 90.

Careful: not even → ÷ 4 ✗

3 Add the digits

We add the digits: 1 + 2 + 9 + 0 is 12.

= 1 + 2 + 9 + 0 = 12

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.

10 = 9 + 1, 100 = 99 + 1

For 3: 12 divided by 3 is 4, nothing left over.

So 3 goes into 1290.

= ÷ 3: 12 ÷ 3 = 4 → yes ✓

For 9: 12 divided by 9 is 1, with 3 left over.

So 9 does not go into 1290.

= ÷ 9: 12 ÷ 9 = 1 r 3 → no ✗

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.

= ÷ 6: ÷ 2 yes ✓ and ÷ 3 yes ✓ → yes ✓
6 = 2 × 3: both

5 Write the answer

So 1290 is divisible by 2, 3, 5, 6 and 10.

Not by 4 or 9.

= divisible by 2, 3, 5, 6, 10

6 Check

Let's check by dividing.

1290 divided by 2 is 645, nothing left over.

1290 ÷ 2 = 645
1290 ÷ 3 = 430
1290 ÷ 5 = 258
1290 ÷ 6 = 215
1290 ÷ 10 = 129
1290 ÷ 4 = 322 r 2 (not divisible)

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.

Answer
= divisible by 2, 3, 5, 6, 10

▶ Watch it solved

Practice

Try each one, then open the answer. Stuck? Open the problem to watch every step.

Easy

  1. is 348 divisible by 2
    Answer
    = yes: 348 ÷ 2 has no remainder
  2. is 735 divisible by 5
    Answer
    = yes: 735 ÷ 5 has no remainder
  3. is 1,460 divisible by 10
    Answer
    = yes: 1460 ÷ 10 has no remainder
  4. is 342 divisible by 3
    Answer
    = yes: 342 ÷ 3 has no remainder
  5. is 73 divisible by 3
    Answer
    = no: 73 ÷ 3 has a remainder
  6. is 51 divisible by 3
    Answer
    = yes: 51 ÷ 3 has no remainder
  7. is 945 divisible by 2
    Answer
    = no: 945 ÷ 2 has a remainder
  8. is 4,215 divisible by 5
    Answer
    = yes: 4215 ÷ 5 has no remainder

Medium

  1. is 2,736 divisible by 9
    Answer
    = yes: 2736 ÷ 9 has no remainder
  2. is 5,742 divisible by 9
    Answer
    = yes: 5742 ÷ 9 has no remainder
  3. is 1,236 divisible by 4
    Answer
    = yes: 1236 ÷ 4 has no remainder
  4. is 5,622 divisible by 4
    Answer
    = no: 5622 ÷ 4 has a remainder
  5. is 7,314 divisible by 6
    Answer
    = yes: 7314 ÷ 6 has no remainder
  6. is 4,326 divisible by 3 and 9
    Answer
    = divisible by 3
  7. is 2,346 divisible by 6 and 9
    Answer
    = divisible by 6
  8. is 1,035 divisible by 6
    Answer
    = no: 1035 ÷ 6 has a remainder

Harder

  1. is 1290 divisible by 2, 3, 4, 5, 6, 9 and 10
    Answer
    = divisible by 2, 3, 5, 6, 10
  2. divisibility tests for 5625
    Answer
    = divisible by 3, 5, 9
  3. divisibility tests for 3,240
    Answer
    = divisible by 2, 3, 4, 5, 6, 9, 10
  4. is 7,866 divisible by 2, 3, 4, 6 and 9
    Answer
    = divisible by 2, 3, 6, 9
  5. divisibility tests for 8,415
    Answer
    = divisible by 3, 5, 9