Factor Calculator

Factors of 352

The factors of 352 are 1, 2, 4, 8, 11, 16, 22, 32, 44, 88, 176, and 352. In total, 352 has 12 factors. Its prime factorization is 2⁵ × 11, and the sum of all its factors is 756.

All factors of 352

Here are all 12 factors of 352, listed from smallest to largest.

1248111622324488176352

Factor pairs of 352

These 6 pairs of whole numbers each multiply to give 352.

1 × 352 = 352
2 × 176 = 352
4 × 88 = 352
8 × 44 = 352
11 × 32 = 352
16 × 22 = 352

Prime factorization of 352

Dividing 352 by the smallest prime at each step gives its prime factorization:

352 ÷ 2 = 176
176 ÷ 2 = 88
88 ÷ 2 = 44
44 ÷ 2 = 22
22 ÷ 2 = 11
11 ÷ 11 = 1
Result: 352 = 2 × 2 × 2 × 2 × 2 × 11 = 2⁵ × 11

The distinct prime factors of 352 are 2, 11. To factorize any other number, use the prime factorization calculator.

Factor tree of 352

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

Factor tree of 3523522176288244222211
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 352

Number of factors12
Sum of factors756
Sum of proper factors404
Prime factorization2⁵ × 11
Prime or composite?Composite
Even or odd?Even
Perfect square?No
Perfect cube?No
ClassificationAbundant

What makes 352 interesting

  • 352 is a composite number, meaning it has more than two factors. It can be written as a product of smaller whole numbers in 6 different ways.
  • 352 is an abundant number: its proper factors sum to 404, which is 52 more than 352 itself.

How to find the factors of 352 yourself

Divide 352 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 √352 ≈ 18.76, because every factor above that pairs with one below it.

352 ÷ 1 = 352 ✓
352 ÷ 2 = 176 ✓
352 ÷ 4 = 88 ✓
352 ÷ 8 = 44 ✓
352 ÷ 11 = 32 ✓
352 ÷ 16 = 22 ✓

Reading both columns gives every factor: 1, 2, 4, 8, 11, 16, 22, 32, 44, 88, 176, 352. The factor calculator does this automatically for any number.

Numbers mathematically connected to 352.

Frequently asked questions about 352

What are the factors of 352?

The factors of 352 are 1, 2, 4, 8, 11, 16, 22, 32, 44, 88, 176, and 352. That is 12 factors in total, counting both 1 and 352.

Is 352 a prime number?

No, 352 is not prime — it is a composite number with 12 factors. A prime number has exactly two factors, but 352 is also divisible by 2.

What is the prime factorization of 352?

The prime factorization of 352 is 2⁵ × 11. Written out in full: 2 × 2 × 2 × 2 × 2 × 11 = 352. Its distinct prime factors are 2, 11.

What two numbers multiply to give 352?

There are 6 pairs of whole numbers that multiply to 352: 1 × 352, 2 × 176, 4 × 88, 8 × 44, 11 × 32, 16 × 22.

What is the sum of the factors of 352?

Adding all the factors of 352 together gives 756. Excluding 352 itself, the proper factors sum to 404.

Is 352 a perfect square?

No, 352 is not a perfect square. There is no whole number that multiplies by itself to give 352. The nearest perfect squares are 324 and 361.

What is the largest factor of 352 other than itself?

The largest factor of 352 apart from 352 itself is 176, since 352 ÷ 176 = 2.

How many factors does 352 have?

352 has 12 factors: 1, 2, 4, 8, 11, 16, 22, 32, 44, 88, 176, and 352. You can verify this from the prime factorization 2⁵ × 11: add 1 to each exponent and multiply, giving 6 × 2 = 12.

Explore more

Try another number in the factor calculator, break 352 down further with the prime factorization calculator, or compare 352 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.