Factor Calculator

Factors of 999

The factors of 999 are 1, 3, 9, 27, 37, 111, 333, and 999. In total, 999 has 8 factors. Its prime factorization is 3³ × 37, and the sum of all its factors is 1520.

All factors of 999

Here are all 8 factors of 999, listed from smallest to largest.

1392737111333999

Factor pairs of 999

These 4 pairs of whole numbers each multiply to give 999.

1 × 999 = 999
3 × 333 = 999
9 × 111 = 999
27 × 37 = 999

Prime factorization of 999

Dividing 999 by the smallest prime at each step gives its prime factorization:

999 ÷ 3 = 333
333 ÷ 3 = 111
111 ÷ 3 = 37
37 ÷ 37 = 1
Result: 999 = 3 × 3 × 3 × 37 = 3³ × 37

The distinct prime factors of 999 are 3, 37. To factorize any other number, use the prime factorization calculator.

Factor tree of 999

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

Factor tree of 99999933333111337
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 999

Number of factors8
Sum of factors1520
Sum of proper factors521
Prime factorization3³ × 37
Prime or composite?Composite
Even or odd?Odd
Perfect square?No
Perfect cube?No
ClassificationDeficient

What makes 999 interesting

  • 999 is a composite number, meaning it has more than two factors. It can be written as a product of smaller whole numbers in 4 different ways.
  • 999 is a deficient number: its proper factors sum to 521, which is 478 less than 999 itself.

How to find the factors of 999 yourself

Divide 999 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 √999 ≈ 31.61, because every factor above that pairs with one below it.

999 ÷ 1 = 999 ✓
999 ÷ 3 = 333 ✓
999 ÷ 9 = 111 ✓
999 ÷ 27 = 37 ✓

Reading both columns gives every factor: 1, 3, 9, 27, 37, 111, 333, 999. The factor calculator does this automatically for any number.

Numbers mathematically connected to 999.

Frequently asked questions about 999

What are the factors of 999?

The factors of 999 are 1, 3, 9, 27, 37, 111, 333, and 999. That is 8 factors in total, counting both 1 and 999.

Is 999 a prime number?

No, 999 is not prime — it is a composite number with 8 factors. A prime number has exactly two factors, but 999 is also divisible by 3.

What is the prime factorization of 999?

The prime factorization of 999 is 3³ × 37. Written out in full: 3 × 3 × 3 × 37 = 999. Its distinct prime factors are 3, 37.

What two numbers multiply to give 999?

There are 4 pairs of whole numbers that multiply to 999: 1 × 999, 3 × 333, 9 × 111, 27 × 37.

What is the sum of the factors of 999?

Adding all the factors of 999 together gives 1520. Excluding 999 itself, the proper factors sum to 521.

Is 999 a perfect square?

No, 999 is not a perfect square. There is no whole number that multiplies by itself to give 999. The nearest perfect squares are 961 and 1024.

What is the largest factor of 999 other than itself?

The largest factor of 999 apart from 999 itself is 333, since 999 ÷ 333 = 3.

How many factors does 999 have?

999 has 8 factors: 1, 3, 9, 27, 37, 111, 333, and 999. You can verify this from the prime factorization 3³ × 37: add 1 to each exponent and multiply, giving 4 × 2 = 8.

Explore more

Try another number in the factor calculator, break 999 down further with the prime factorization calculator, or compare 999 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.