Factor Calculator

Factors of 872

The factors of 872 are 1, 2, 4, 8, 109, 218, 436, and 872. In total, 872 has 8 factors. Its prime factorization is 2³ × 109, and the sum of all its factors is 1650.

All factors of 872

Here are all 8 factors of 872, listed from smallest to largest.

1248109218436872

Factor pairs of 872

These 4 pairs of whole numbers each multiply to give 872.

1 × 872 = 872
2 × 436 = 872
4 × 218 = 872
8 × 109 = 872

Prime factorization of 872

Dividing 872 by the smallest prime at each step gives its prime factorization:

872 ÷ 2 = 436
436 ÷ 2 = 218
218 ÷ 2 = 109
109 ÷ 109 = 1
Result: 872 = 2 × 2 × 2 × 109 = 2³ × 109

The distinct prime factors of 872 are 2, 109. To factorize any other number, use the prime factorization calculator.

Factor tree of 872

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

Factor tree of 872872243622182109
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 872

Number of factors8
Sum of factors1650
Sum of proper factors778
Prime factorization2³ × 109
Prime or composite?Composite
Even or odd?Even
Perfect square?No
Perfect cube?No
ClassificationDeficient

What makes 872 interesting

  • 872 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.
  • 872 is a deficient number: its proper factors sum to 778, which is 94 less than 872 itself.

How to find the factors of 872 yourself

Divide 872 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 √872 ≈ 29.53, because every factor above that pairs with one below it.

872 ÷ 1 = 872 ✓
872 ÷ 2 = 436 ✓
872 ÷ 4 = 218 ✓
872 ÷ 8 = 109 ✓

Reading both columns gives every factor: 1, 2, 4, 8, 109, 218, 436, 872. The factor calculator does this automatically for any number.

Numbers mathematically connected to 872.

Frequently asked questions about 872

What are the factors of 872?

The factors of 872 are 1, 2, 4, 8, 109, 218, 436, and 872. That is 8 factors in total, counting both 1 and 872.

Is 872 a prime number?

No, 872 is not prime — it is a composite number with 8 factors. A prime number has exactly two factors, but 872 is also divisible by 2.

What is the prime factorization of 872?

The prime factorization of 872 is 2³ × 109. Written out in full: 2 × 2 × 2 × 109 = 872. Its distinct prime factors are 2, 109.

What two numbers multiply to give 872?

There are 4 pairs of whole numbers that multiply to 872: 1 × 872, 2 × 436, 4 × 218, 8 × 109.

What is the sum of the factors of 872?

Adding all the factors of 872 together gives 1650. Excluding 872 itself, the proper factors sum to 778.

Is 872 a perfect square?

No, 872 is not a perfect square. There is no whole number that multiplies by itself to give 872. The nearest perfect squares are 841 and 900.

What is the largest factor of 872 other than itself?

The largest factor of 872 apart from 872 itself is 436, since 872 ÷ 436 = 2.

How many factors does 872 have?

872 has 8 factors: 1, 2, 4, 8, 109, 218, 436, and 872. You can verify this from the prime factorization 2³ × 109: add 1 to each exponent and multiply, giving 4 × 2 = 8.

Explore more

Try another number in the factor calculator, break 872 down further with the prime factorization calculator, or compare 872 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.