Factor Calculator

Factors of 801

The factors of 801 are 1, 3, 9, 89, 267, and 801. In total, 801 has 6 factors. Its prime factorization is 3² × 89, and the sum of all its factors is 1170.

All factors of 801

Here are all 6 factors of 801, listed from smallest to largest.

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Factor pairs of 801

These 3 pairs of whole numbers each multiply to give 801.

1 × 801 = 801
3 × 267 = 801
9 × 89 = 801

Prime factorization of 801

Dividing 801 by the smallest prime at each step gives its prime factorization:

801 ÷ 3 = 267
267 ÷ 3 = 89
89 ÷ 89 = 1
Result: 801 = 3 × 3 × 89 = 3² × 89

The distinct prime factors of 801 are 3, 89. To factorize any other number, use the prime factorization calculator.

Factor tree of 801

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

Factor tree of 8018013267389
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 801

Number of factors6
Sum of factors1170
Sum of proper factors369
Prime factorization3² × 89
Prime or composite?Composite
Even or odd?Odd
Perfect square?No
Perfect cube?No
ClassificationDeficient

What makes 801 interesting

  • 801 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.
  • 801 is a deficient number: its proper factors sum to 369, which is 432 less than 801 itself.

How to find the factors of 801 yourself

Divide 801 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 √801 ≈ 28.30, because every factor above that pairs with one below it.

801 ÷ 1 = 801 ✓
801 ÷ 3 = 267 ✓
801 ÷ 9 = 89 ✓

Reading both columns gives every factor: 1, 3, 9, 89, 267, 801. The factor calculator does this automatically for any number.

Numbers mathematically connected to 801.

Frequently asked questions about 801

What are the factors of 801?

The factors of 801 are 1, 3, 9, 89, 267, and 801. That is 6 factors in total, counting both 1 and 801.

Is 801 a prime number?

No, 801 is not prime — it is a composite number with 6 factors. A prime number has exactly two factors, but 801 is also divisible by 3.

What is the prime factorization of 801?

The prime factorization of 801 is 3² × 89. Written out in full: 3 × 3 × 89 = 801. Its distinct prime factors are 3, 89.

What two numbers multiply to give 801?

There are 3 pairs of whole numbers that multiply to 801: 1 × 801, 3 × 267, 9 × 89.

What is the sum of the factors of 801?

Adding all the factors of 801 together gives 1170. Excluding 801 itself, the proper factors sum to 369.

Is 801 a perfect square?

No, 801 is not a perfect square. There is no whole number that multiplies by itself to give 801. The nearest perfect squares are 784 and 841.

What is the largest factor of 801 other than itself?

The largest factor of 801 apart from 801 itself is 267, since 801 ÷ 267 = 3.

How many factors does 801 have?

801 has 6 factors: 1, 3, 9, 89, 267, and 801. You can verify this from the prime factorization 3² × 89: add 1 to each exponent and multiply, giving 3 × 2 = 6.

Explore more

Try another number in the factor calculator, break 801 down further with the prime factorization calculator, or compare 801 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.