Factor Calculator

Factors of 820

The factors of 820 are 1, 2, 4, 5, 10, 20, 41, 82, 164, 205, 410, and 820. In total, 820 has 12 factors. Its prime factorization is 2² × 5 × 41, and the sum of all its factors is 1764.

All factors of 820

Here are all 12 factors of 820, listed from smallest to largest.

124510204182164205410820

Factor pairs of 820

These 6 pairs of whole numbers each multiply to give 820.

1 × 820 = 820
2 × 410 = 820
4 × 205 = 820
5 × 164 = 820
10 × 82 = 820
20 × 41 = 820

Prime factorization of 820

Dividing 820 by the smallest prime at each step gives its prime factorization:

820 ÷ 2 = 410
410 ÷ 2 = 205
205 ÷ 5 = 41
41 ÷ 41 = 1
Result: 820 = 2 × 2 × 5 × 41 = 2² × 5 × 41

The distinct prime factors of 820 are 2, 5, 41. To factorize any other number, use the prime factorization calculator.

Factor tree of 820

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

Factor tree of 82082024102205541
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 820

Number of factors12
Sum of factors1764
Sum of proper factors944
Prime factorization2² × 5 × 41
Prime or composite?Composite
Even or odd?Even
Perfect square?No
Perfect cube?No
ClassificationAbundant

What makes 820 interesting

  • 820 is a composite number, meaning it has more than two factors. It can be written as a product of smaller whole numbers in 6 different ways.
  • 820 is an abundant number: its proper factors sum to 944, which is 124 more than 820 itself.
  • 820 is a triangular number — it is the sum of the first 40 whole numbers (1 + 2 + … + 40 = 820).
  • 820 has 3 distinct prime factors (2, 5, 41), which is why it has so many divisors.

How to find the factors of 820 yourself

Divide 820 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 √820 ≈ 28.64, because every factor above that pairs with one below it.

820 ÷ 1 = 820 ✓
820 ÷ 2 = 410 ✓
820 ÷ 4 = 205 ✓
820 ÷ 5 = 164 ✓
820 ÷ 10 = 82 ✓
820 ÷ 20 = 41 ✓

Reading both columns gives every factor: 1, 2, 4, 5, 10, 20, 41, 82, 164, 205, 410, 820. The factor calculator does this automatically for any number.

Numbers mathematically connected to 820.

Frequently asked questions about 820

What are the factors of 820?

The factors of 820 are 1, 2, 4, 5, 10, 20, 41, 82, 164, 205, 410, and 820. That is 12 factors in total, counting both 1 and 820.

Is 820 a prime number?

No, 820 is not prime — it is a composite number with 12 factors. A prime number has exactly two factors, but 820 is also divisible by 2.

What is the prime factorization of 820?

The prime factorization of 820 is 2² × 5 × 41. Written out in full: 2 × 2 × 5 × 41 = 820. Its distinct prime factors are 2, 5, 41.

What two numbers multiply to give 820?

There are 6 pairs of whole numbers that multiply to 820: 1 × 820, 2 × 410, 4 × 205, 5 × 164, 10 × 82, 20 × 41.

What is the sum of the factors of 820?

Adding all the factors of 820 together gives 1764. Excluding 820 itself, the proper factors sum to 944.

Is 820 a perfect square?

No, 820 is not a perfect square. There is no whole number that multiplies by itself to give 820. The nearest perfect squares are 784 and 841.

What is the largest factor of 820 other than itself?

The largest factor of 820 apart from 820 itself is 410, since 820 ÷ 410 = 2.

How many factors does 820 have?

820 has 12 factors: 1, 2, 4, 5, 10, 20, 41, 82, 164, 205, 410, and 820. You can verify this from the prime factorization 2² × 5 × 41: add 1 to each exponent and multiply, giving 3 × 2 × 2 = 12.

Explore more

Try another number in the factor calculator, break 820 down further with the prime factorization calculator, or compare 820 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.