Factor Calculator

Factors of 172

The factors of 172 are 1, 2, 4, 43, 86, and 172. In total, 172 has 6 factors. Its prime factorization is 2² × 43, and the sum of all its factors is 308.

All factors of 172

Here are all 6 factors of 172, listed from smallest to largest.

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Factor pairs of 172

These 3 pairs of whole numbers each multiply to give 172.

1 × 172 = 172
2 × 86 = 172
4 × 43 = 172

Prime factorization of 172

Dividing 172 by the smallest prime at each step gives its prime factorization:

172 ÷ 2 = 86
86 ÷ 2 = 43
43 ÷ 43 = 1
Result: 172 = 2 × 2 × 43 = 2² × 43

The distinct prime factors of 172 are 2, 43. To factorize any other number, use the prime factorization calculator.

Factor tree of 172

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

Factor tree of 172172286243
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 172

Number of factors6
Sum of factors308
Sum of proper factors136
Prime factorization2² × 43
Prime or composite?Composite
Even or odd?Even
Perfect square?No
Perfect cube?No
ClassificationDeficient

What makes 172 interesting

  • 172 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.
  • 172 is a deficient number: its proper factors sum to 136, which is 36 less than 172 itself.

How to find the factors of 172 yourself

Divide 172 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 √172 ≈ 13.11, because every factor above that pairs with one below it.

172 ÷ 1 = 172 ✓
172 ÷ 2 = 86 ✓
172 ÷ 4 = 43 ✓

Reading both columns gives every factor: 1, 2, 4, 43, 86, 172. The factor calculator does this automatically for any number.

Numbers mathematically connected to 172.

Frequently asked questions about 172

What are the factors of 172?

The factors of 172 are 1, 2, 4, 43, 86, and 172. That is 6 factors in total, counting both 1 and 172.

Is 172 a prime number?

No, 172 is not prime — it is a composite number with 6 factors. A prime number has exactly two factors, but 172 is also divisible by 2.

What is the prime factorization of 172?

The prime factorization of 172 is 2² × 43. Written out in full: 2 × 2 × 43 = 172. Its distinct prime factors are 2, 43.

What two numbers multiply to give 172?

There are 3 pairs of whole numbers that multiply to 172: 1 × 172, 2 × 86, 4 × 43.

What is the sum of the factors of 172?

Adding all the factors of 172 together gives 308. Excluding 172 itself, the proper factors sum to 136.

Is 172 a perfect square?

No, 172 is not a perfect square. There is no whole number that multiplies by itself to give 172. The nearest perfect squares are 169 and 196.

What is the largest factor of 172 other than itself?

The largest factor of 172 apart from 172 itself is 86, since 172 ÷ 86 = 2.

How many factors does 172 have?

172 has 6 factors: 1, 2, 4, 43, 86, and 172. You can verify this from the prime factorization 2² × 43: add 1 to each exponent and multiply, giving 3 × 2 = 6.

Explore more

Try another number in the factor calculator, break 172 down further with the prime factorization calculator, or compare 172 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.