Factor Calculator

Factors of 208

The factors of 208 are 1, 2, 4, 8, 13, 16, 26, 52, 104, and 208. In total, 208 has 10 factors. Its prime factorization is 2⁴ × 13, and the sum of all its factors is 434.

All factors of 208

Here are all 10 factors of 208, listed from smallest to largest.

124813162652104208

Factor pairs of 208

These 5 pairs of whole numbers each multiply to give 208.

1 × 208 = 208
2 × 104 = 208
4 × 52 = 208
8 × 26 = 208
13 × 16 = 208

Prime factorization of 208

Dividing 208 by the smallest prime at each step gives its prime factorization:

208 ÷ 2 = 104
104 ÷ 2 = 52
52 ÷ 2 = 26
26 ÷ 2 = 13
13 ÷ 13 = 1
Result: 208 = 2 × 2 × 2 × 2 × 13 = 2⁴ × 13

The distinct prime factors of 208 are 2, 13. To factorize any other number, use the prime factorization calculator.

Factor tree of 208

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

Factor tree of 2082082104252226213
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 208

Number of factors10
Sum of factors434
Sum of proper factors226
Prime factorization2⁴ × 13
Prime or composite?Composite
Even or odd?Even
Perfect square?No
Perfect cube?No
ClassificationAbundant

What makes 208 interesting

  • 208 is a composite number, meaning it has more than two factors. It can be written as a product of smaller whole numbers in 5 different ways.
  • 208 is an abundant number: its proper factors sum to 226, which is 18 more than 208 itself.

How to find the factors of 208 yourself

Divide 208 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 √208 ≈ 14.42, because every factor above that pairs with one below it.

208 ÷ 1 = 208 ✓
208 ÷ 2 = 104 ✓
208 ÷ 4 = 52 ✓
208 ÷ 8 = 26 ✓
208 ÷ 13 = 16 ✓

Reading both columns gives every factor: 1, 2, 4, 8, 13, 16, 26, 52, 104, 208. The factor calculator does this automatically for any number.

Numbers mathematically connected to 208.

Frequently asked questions about 208

What are the factors of 208?

The factors of 208 are 1, 2, 4, 8, 13, 16, 26, 52, 104, and 208. That is 10 factors in total, counting both 1 and 208.

Is 208 a prime number?

No, 208 is not prime — it is a composite number with 10 factors. A prime number has exactly two factors, but 208 is also divisible by 2.

What is the prime factorization of 208?

The prime factorization of 208 is 2⁴ × 13. Written out in full: 2 × 2 × 2 × 2 × 13 = 208. Its distinct prime factors are 2, 13.

What two numbers multiply to give 208?

There are 5 pairs of whole numbers that multiply to 208: 1 × 208, 2 × 104, 4 × 52, 8 × 26, 13 × 16.

What is the sum of the factors of 208?

Adding all the factors of 208 together gives 434. Excluding 208 itself, the proper factors sum to 226.

Is 208 a perfect square?

No, 208 is not a perfect square. There is no whole number that multiplies by itself to give 208. The nearest perfect squares are 196 and 225.

What is the largest factor of 208 other than itself?

The largest factor of 208 apart from 208 itself is 104, since 208 ÷ 104 = 2.

How many factors does 208 have?

208 has 10 factors: 1, 2, 4, 8, 13, 16, 26, 52, 104, and 208. You can verify this from the prime factorization 2⁴ × 13: add 1 to each exponent and multiply, giving 5 × 2 = 10.

Explore more

Try another number in the factor calculator, break 208 down further with the prime factorization calculator, or compare 208 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.