Factor Calculator

Factors of 351

The factors of 351 are 1, 3, 9, 13, 27, 39, 117, and 351. In total, 351 has 8 factors. Its prime factorization is 3³ × 13, and the sum of all its factors is 560.

All factors of 351

Here are all 8 factors of 351, listed from smallest to largest.

139132739117351

Factor pairs of 351

These 4 pairs of whole numbers each multiply to give 351.

1 × 351 = 351
3 × 117 = 351
9 × 39 = 351
13 × 27 = 351

Prime factorization of 351

Dividing 351 by the smallest prime at each step gives its prime factorization:

351 ÷ 3 = 117
117 ÷ 3 = 39
39 ÷ 3 = 13
13 ÷ 13 = 1
Result: 351 = 3 × 3 × 3 × 13 = 3³ × 13

The distinct prime factors of 351 are 3, 13. To factorize any other number, use the prime factorization calculator.

Factor tree of 351

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

Factor tree of 3513513117339313
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 351

Number of factors8
Sum of factors560
Sum of proper factors209
Prime factorization3³ × 13
Prime or composite?Composite
Even or odd?Odd
Perfect square?No
Perfect cube?No
ClassificationDeficient

What makes 351 interesting

  • 351 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.
  • 351 is a deficient number: its proper factors sum to 209, which is 142 less than 351 itself.
  • 351 is a triangular number — it is the sum of the first 26 whole numbers (1 + 2 + … + 26 = 351).

How to find the factors of 351 yourself

Divide 351 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 √351 ≈ 18.73, because every factor above that pairs with one below it.

351 ÷ 1 = 351 ✓
351 ÷ 3 = 117 ✓
351 ÷ 9 = 39 ✓
351 ÷ 13 = 27 ✓

Reading both columns gives every factor: 1, 3, 9, 13, 27, 39, 117, 351. The factor calculator does this automatically for any number.

Numbers mathematically connected to 351.

Frequently asked questions about 351

What are the factors of 351?

The factors of 351 are 1, 3, 9, 13, 27, 39, 117, and 351. That is 8 factors in total, counting both 1 and 351.

Is 351 a prime number?

No, 351 is not prime — it is a composite number with 8 factors. A prime number has exactly two factors, but 351 is also divisible by 3.

What is the prime factorization of 351?

The prime factorization of 351 is 3³ × 13. Written out in full: 3 × 3 × 3 × 13 = 351. Its distinct prime factors are 3, 13.

What two numbers multiply to give 351?

There are 4 pairs of whole numbers that multiply to 351: 1 × 351, 3 × 117, 9 × 39, 13 × 27.

What is the sum of the factors of 351?

Adding all the factors of 351 together gives 560. Excluding 351 itself, the proper factors sum to 209.

Is 351 a perfect square?

No, 351 is not a perfect square. There is no whole number that multiplies by itself to give 351. The nearest perfect squares are 324 and 361.

What is the largest factor of 351 other than itself?

The largest factor of 351 apart from 351 itself is 117, since 351 ÷ 117 = 3.

How many factors does 351 have?

351 has 8 factors: 1, 3, 9, 13, 27, 39, 117, and 351. You can verify this from the prime factorization 3³ × 13: add 1 to each exponent and multiply, giving 4 × 2 = 8.

Explore more

Try another number in the factor calculator, break 351 down further with the prime factorization calculator, or compare 351 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.