Factor Calculator

Factors of 870

The factors of 870 are 1, 2, 3, 5, 6, 10, 15, 29, 30, 58, 87, 145, 174, 290, 435, and 870. In total, 870 has 16 factors. Its prime factorization is 2 × 3 × 5 × 29, and the sum of all its factors is 2160.

All factors of 870

Here are all 16 factors of 870, listed from smallest to largest.

12356101529305887145174290435870

Factor pairs of 870

These 8 pairs of whole numbers each multiply to give 870.

1 × 870 = 870
2 × 435 = 870
3 × 290 = 870
5 × 174 = 870
6 × 145 = 870
10 × 87 = 870
15 × 58 = 870
29 × 30 = 870

Prime factorization of 870

Dividing 870 by the smallest prime at each step gives its prime factorization:

870 ÷ 2 = 435
435 ÷ 3 = 145
145 ÷ 5 = 29
29 ÷ 29 = 1
Result: 870 = 2 × 3 × 5 × 29 = 2 × 3 × 5 × 29

The distinct prime factors of 870 are 2, 3, 5, 29. To factorize any other number, use the prime factorization calculator.

Factor tree of 870

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

Factor tree of 87087024353145529
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 870

Number of factors16
Sum of factors2160
Sum of proper factors1290
Prime factorization2 × 3 × 5 × 29
Prime or composite?Composite
Even or odd?Even
Perfect square?No
Perfect cube?No
ClassificationAbundant

What makes 870 interesting

  • 870 is a composite number, meaning it has more than two factors. It can be written as a product of smaller whole numbers in 8 different ways.
  • 870 is an abundant number: its proper factors sum to 1290, which is 420 more than 870 itself.
  • 870 has 4 distinct prime factors (2, 3, 5, 29), which is why it has so many divisors.

How to find the factors of 870 yourself

Divide 870 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 √870 ≈ 29.50, because every factor above that pairs with one below it.

870 ÷ 1 = 870 ✓
870 ÷ 2 = 435 ✓
870 ÷ 3 = 290 ✓
870 ÷ 5 = 174 ✓
870 ÷ 6 = 145 ✓
870 ÷ 10 = 87 ✓
870 ÷ 15 = 58 ✓
870 ÷ 29 = 30 ✓

Reading both columns gives every factor: 1, 2, 3, 5, 6, 10, 15, 29, 30, 58, 87, 145, 174, 290, 435, 870. The factor calculator does this automatically for any number.

Numbers mathematically connected to 870.

Frequently asked questions about 870

What are the factors of 870?

The factors of 870 are 1, 2, 3, 5, 6, 10, 15, 29, 30, 58, 87, 145, 174, 290, 435, and 870. That is 16 factors in total, counting both 1 and 870.

Is 870 a prime number?

No, 870 is not prime — it is a composite number with 16 factors. A prime number has exactly two factors, but 870 is also divisible by 2.

What is the prime factorization of 870?

The prime factorization of 870 is 2 × 3 × 5 × 29. Written out in full: 2 × 3 × 5 × 29 = 870. Its distinct prime factors are 2, 3, 5, 29.

What two numbers multiply to give 870?

There are 8 pairs of whole numbers that multiply to 870: 1 × 870, 2 × 435, 3 × 290, 5 × 174, 6 × 145, 10 × 87, 15 × 58, 29 × 30.

What is the sum of the factors of 870?

Adding all the factors of 870 together gives 2160. Excluding 870 itself, the proper factors sum to 1290.

Is 870 a perfect square?

No, 870 is not a perfect square. There is no whole number that multiplies by itself to give 870. The nearest perfect squares are 841 and 900.

What is the largest factor of 870 other than itself?

The largest factor of 870 apart from 870 itself is 435, since 870 ÷ 435 = 2.

How many factors does 870 have?

870 has 16 factors: 1, 2, 3, 5, 6, 10, 15, 29, 30, 58, 87, 145, 174, 290, 435, and 870. You can verify this from the prime factorization 2 × 3 × 5 × 29: add 1 to each exponent and multiply, giving 2 × 2 × 2 × 2 = 16.

Explore more

Try another number in the factor calculator, break 870 down further with the prime factorization calculator, or compare 870 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.