Factor Calculator

Factors of 338

The factors of 338 are 1, 2, 13, 26, 169, and 338. In total, 338 has 6 factors. Its prime factorization is 2 × 13², and the sum of all its factors is 549.

All factors of 338

Here are all 6 factors of 338, listed from smallest to largest.

121326169338

Factor pairs of 338

These 3 pairs of whole numbers each multiply to give 338.

1 × 338 = 338
2 × 169 = 338
13 × 26 = 338

Prime factorization of 338

Dividing 338 by the smallest prime at each step gives its prime factorization:

338 ÷ 2 = 169
169 ÷ 13 = 13
13 ÷ 13 = 1
Result: 338 = 2 × 13 × 13 = 2 × 13²

The distinct prime factors of 338 are 2, 13. To factorize any other number, use the prime factorization calculator.

Factor tree of 338

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

Factor tree of 33833821691313
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 338

Number of factors6
Sum of factors549
Sum of proper factors211
Prime factorization2 × 13²
Prime or composite?Composite
Even or odd?Even
Perfect square?No
Perfect cube?No
ClassificationDeficient

What makes 338 interesting

  • 338 is a composite number, meaning it has more than two factors. It can be written as a product of smaller whole numbers in 3 different ways.
  • 338 is a deficient number: its proper factors sum to 211, which is 127 less than 338 itself.

How to find the factors of 338 yourself

Divide 338 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 √33818.38, because every factor above that pairs with one below it.

338 ÷ 1 = 338
338 ÷ 2 = 169
338 ÷ 13 = 26

Reading both columns gives every factor: 1, 2, 13, 26, 169, 338. The factor calculator does this automatically for any number.

Frequently asked questions about 338

What are the factors of 338?

The factors of 338 are 1, 2, 13, 26, 169, and 338. That is 6 factors in total, counting both 1 and 338.

Is 338 a prime number?

No, 338 is not prime — it is a composite number with 6 factors. A prime number has exactly two factors, but 338 is also divisible by 2.

What is the prime factorization of 338?

The prime factorization of 338 is 2 × 13². Written out in full: 2 × 13 × 13 = 338. Its distinct prime factors are 2, 13.

What two numbers multiply to give 338?

There are 3 pairs of whole numbers that multiply to 338: 1 × 338, 2 × 169, 13 × 26.

What is the sum of the factors of 338?

Adding all the factors of 338 together gives 549. Excluding 338 itself, the proper factors sum to 211.

Is 338 a perfect square?

No, 338 is not a perfect square. There is no whole number that multiplies by itself to give 338. The nearest perfect squares are 324 and 361.

What is the largest factor of 338 other than itself?

The largest factor of 338 apart from 338 itself is 169, since 338 ÷ 169 = 2.

How many factors does 338 have?

338 has 6 factors: 1, 2, 13, 26, 169, and 338. You can verify this from the prime factorization 2 × 13²: add 1 to each exponent and multiply, giving 2 × 3 = 6.

Explore more

Try another number in the factor calculator, break 338 down further with the prime factorization calculator, or compare 338 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.