Factors of 9

The factors of 9 are 1, 3, and 9. In total, 9 has 3 factors. Its prime factorization is 3², and the sum of all its factors is 13. 9 is also a perfect square, equal to 3 × 3.

All factors of 9

Here are all 3 factors of 9, listed from smallest to largest.

139

Factor pairs of 9

These 2 pairs of whole numbers each multiply to give 9.

1 × 9 = 9

3 × 3 = 9

Notice the pair (3, 3) — because 9 is a perfect square, this pair uses the same number twice.

Prime factorization of 9

Dividing 9 by the smallest prime at each step gives its prime factorization:

9 ÷ 3 = 3

3 ÷ 3 = 1

Result: 9 = 3 × 3 = 3²

The distinct prime factors of 9 are 3. To factorize any other number, use the prime factorization calculator.

Factor tree of 9

A factor tree shows the same prime factorization visually. Each composite branch splits until every endpoint is a prime number.

Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 9

Number of factors	3
Sum of factors	13
Sum of proper factors	4
Prime factorization	3²
Prime or composite?	Composite
Even or odd?	Odd
Perfect square?	Yes (3²)
Perfect cube?	No
Classification	Deficient

What makes 9 interesting

9 is a composite number, meaning it has more than two factors. It can be written as a product of smaller whole numbers in 2 different ways.
9 is a perfect square: 3 × 3 = 9. This is why it has an odd number of factors (3) — the pair (3, 3) counts only once.
9 is a deficient number: its proper factors sum to 4, which is 5 less than 9 itself.
9 is a prime power: it is 3 raised to the power of 2. All of its factors are powers of 3.

How to find the factors of 9 yourself

Divide 9 by each whole number starting from 1. Whenever the division leaves no remainder, both the divisor and the quotient are factors. You only need to test up to √9 ≈ 3.00, because every factor above that pairs with one below it.

9 ÷ 1 = 9 ✓

9 ÷ 3 = 3 ✓

Reading both columns gives every factor: 1, 3, 9. The factor calculator does this automatically for any number.

Numbers mathematically connected to 9.

Frequently asked questions about 9

What are the factors of 9?

The factors of 9 are 1, 3, and 9. That is 3 factors in total, counting both 1 and 9.

Is 9 a prime number?

No, 9 is not prime — it is a composite number with 3 factors. A prime number has exactly two factors, but 9 is also divisible by 3.

What is the prime factorization of 9?

The prime factorization of 9 is 3². Written out in full: 3 × 3 = 9. Its distinct prime factors are 3.

What two numbers multiply to give 9?

There are 2 pairs of whole numbers that multiply to 9: 1 × 9, 3 × 3.

What is the sum of the factors of 9?

Adding all the factors of 9 together gives 13. Excluding 9 itself, the proper factors sum to 4.

Is 9 a perfect square?

Yes, 9 is a perfect square. It equals 3 × 3. Perfect squares always have an odd number of factors — 9 has 3.

What is the largest factor of 9 other than itself?

The largest factor of 9 apart from 9 itself is 3, since 9 ÷ 3 = 3.

How many factors does 9 have?

9 has 3 factors: 1, 3, and 9. You can verify this from the prime factorization 3²: add 1 to each exponent and multiply, giving 3 = 3.

Explore more

Try another number in the factor calculator, break 9 down further with the prime factorization calculator, or compare 9 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.