What is the prime factorization of 9?

9 = 3 × 3 = 3². The only prime factor of 9 is 3.

No. 9 is composite because 3 × 3 = 9, so it has three factors instead of two.

What is the divisibility rule for 9?

A number is divisible by 9 when its digits add up to a multiple of 9. For example, 729 has digits that add to 18, so 729 is divisible by 9.

Factors of 9 - Pairs, Prime Factorization & Examples

Q: What are the factors of 9?

The factors of 9 are 1, 3 and 9. It has three factors.

What Are the Factors of 9?

Arrange 9 tiles into a square and you get a tidy 3 by 3 grid. You could also line them up in a single row of 9. Those layouts are the factors in action. A factor is a whole number that divides another number exactly, leaving nothing behind.

The factors of 9 are 1, 3 and 9. There are three of them, and 9 is a perfect square.

Factor Pairs of 9

Hunt for pairs that multiply to 9 rather than testing every number.

Handwritten notebook page titled Factors of 9 showing 1 × 9 = 9 and 3 × 3 = 9, with the factors 1, 3 and 9 circled in red and the note 3 factors — The pairs of 9. In 3 × 3 the same number appears twice.

Start with 1 × 9. Every number has this pair.
Try 2. It leaves a remainder of 1, so skip it.
Try 3. Since 9 ÷ 3 = 3, write 3 × 3. Both partners are the same, so you have met in the middle and you are done.

Prime Factorization of 9

Prime factors show what 9 is made from. Split it into two numbers and check whether each is prime.

Handwritten factor tree of 9 splitting into two red-circled 3s, with 9 = 3 × 3 = 3² written below in green — Factor tree of 9. Both branches stop at the prime 3.

So 9 = 3 × 3 = 3². The only prime factor is 3. Add 1 to the exponent, 2 + 1 = 3, and you get the three factors.

A quick rule: divisibility by 9

Add up the digits of any number. If the total is a multiple of 9, the number divides by 9. Take 5,238: 5 + 2 + 3 + 8 = 18, so 5,238 is a multiple of 9. This is one of the handiest mental checks there is.

Is 9 a Prime or Composite Number?

Composite. Many people assume odd numbers are prime, but 9 has three factors, not two. It is the smallest odd composite number.

Real-Life Uses of the Factors of 9

Baseball. A game has 9 innings and a team fields 9 players.
Grids. A tic-tac-toe board and a sudoku box both have 9 squares in a 3 by 3 layout.
Sharing. Nine apples can be split fairly between 3 people, 3 each.

Common Factors of 9 With Other Numbers

The factors of 12 are 1, 2, 3, 4, 6 and 12. It shares 1 and 3 with 9, so the GCF is 3. That reduces 9/12 to 3/4.

Quick Practice

Which of these are factors of 9: 2, 3 or 6? Only 3. Test 18 yourself using the digit rule, then confirm with the calculator.

Factors of 9