Factor Calculator

Factors of 990

The factors of 990 are 1, 2, 3, 5, 6, 9, 10, 11, 15, 18, 22, 30, 33, 45, 55, 66, 90, 99, 110, 165, 198, 330, 495, and 990. In total, 990 has 24 factors. Its prime factorization is 2 × 3² × 5 × 11, and the sum of all its factors is 2808.

All factors of 990

Here are all 24 factors of 990, listed from smallest to largest.

123569101115182230334555669099110165198330495990

Factor pairs of 990

These 12 pairs of whole numbers each multiply to give 990.

1 × 990 = 990
2 × 495 = 990
3 × 330 = 990
5 × 198 = 990
6 × 165 = 990
9 × 110 = 990
10 × 99 = 990
11 × 90 = 990
15 × 66 = 990
18 × 55 = 990
22 × 45 = 990
30 × 33 = 990

Prime factorization of 990

Dividing 990 by the smallest prime at each step gives its prime factorization:

990 ÷ 2 = 495
495 ÷ 3 = 165
165 ÷ 3 = 55
55 ÷ 5 = 11
11 ÷ 11 = 1
Result: 990 = 2 × 3 × 3 × 5 × 11 = 2 × 3² × 5 × 11

The distinct prime factors of 990 are 2, 3, 5, 11. To factorize any other number, use the prime factorization calculator.

Factor tree of 990

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

Factor tree of 99099024953165355511
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 990

Number of factors24
Sum of factors2808
Sum of proper factors1818
Prime factorization2 × 3² × 5 × 11
Prime or composite?Composite
Even or odd?Even
Perfect square?No
Perfect cube?No
ClassificationAbundant

What makes 990 interesting

  • 990 is a composite number, meaning it has more than two factors. It can be written as a product of smaller whole numbers in 12 different ways.
  • 990 is an abundant number: its proper factors sum to 1818, which is 828 more than 990 itself.
  • 990 is a triangular number — it is the sum of the first 44 whole numbers (1 + 2 + … + 44 = 990).
  • 990 has 4 distinct prime factors (2, 3, 5, 11), which is why it has so many divisors.

How to find the factors of 990 yourself

Divide 990 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 √990 ≈ 31.46, because every factor above that pairs with one below it.

990 ÷ 1 = 990 ✓
990 ÷ 2 = 495 ✓
990 ÷ 3 = 330 ✓
990 ÷ 5 = 198 ✓
990 ÷ 6 = 165 ✓
990 ÷ 9 = 110 ✓
990 ÷ 10 = 99 ✓
990 ÷ 11 = 90 ✓
990 ÷ 15 = 66 ✓
990 ÷ 18 = 55 ✓
990 ÷ 22 = 45 ✓
990 ÷ 30 = 33 ✓

Reading both columns gives every factor: 1, 2, 3, 5, 6, 9, 10, 11, 15, 18, 22, 30, 33, 45, 55, 66, 90, 99, 110, 165, 198, 330, 495, 990. The factor calculator does this automatically for any number.

Numbers mathematically connected to 990.

Frequently asked questions about 990

What are the factors of 990?

The factors of 990 are 1, 2, 3, 5, 6, 9, 10, 11, 15, 18, 22, 30, 33, 45, 55, 66, 90, 99, 110, 165, 198, 330, 495, and 990. That is 24 factors in total, counting both 1 and 990.

Is 990 a prime number?

No, 990 is not prime — it is a composite number with 24 factors. A prime number has exactly two factors, but 990 is also divisible by 2.

What is the prime factorization of 990?

The prime factorization of 990 is 2 × 3² × 5 × 11. Written out in full: 2 × 3 × 3 × 5 × 11 = 990. Its distinct prime factors are 2, 3, 5, 11.

What two numbers multiply to give 990?

There are 12 pairs of whole numbers that multiply to 990: 1 × 990, 2 × 495, 3 × 330, 5 × 198, 6 × 165, 9 × 110, 10 × 99, 11 × 90, 15 × 66, 18 × 55, 22 × 45, 30 × 33.

What is the sum of the factors of 990?

Adding all the factors of 990 together gives 2808. Excluding 990 itself, the proper factors sum to 1818.

Is 990 a perfect square?

No, 990 is not a perfect square. There is no whole number that multiplies by itself to give 990. The nearest perfect squares are 961 and 1024.

What is the largest factor of 990 other than itself?

The largest factor of 990 apart from 990 itself is 495, since 990 ÷ 495 = 2.

How many factors does 990 have?

990 has 24 factors: 1, 2, 3, 5, 6, 9, 10, 11, 15, 18, 22, 30, 33, 45, 55, 66, 90, 99, 110, 165, 198, 330, 495, and 990. You can verify this from the prime factorization 2 × 3² × 5 × 11: add 1 to each exponent and multiply, giving 2 × 3 × 2 × 2 = 24.

Explore more

Try another number in the factor calculator, break 990 down further with the prime factorization calculator, or compare 990 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.