Factor Calculator

Factors of 891

The factors of 891 are 1, 3, 9, 11, 27, 33, 81, 99, 297, and 891. In total, 891 has 10 factors. Its prime factorization is 3⁴ × 11, and the sum of all its factors is 1452.

All factors of 891

Here are all 10 factors of 891, listed from smallest to largest.

1391127338199297891

Factor pairs of 891

These 5 pairs of whole numbers each multiply to give 891.

1 × 891 = 891
3 × 297 = 891
9 × 99 = 891
11 × 81 = 891
27 × 33 = 891

Prime factorization of 891

Dividing 891 by the smallest prime at each step gives its prime factorization:

891 ÷ 3 = 297
297 ÷ 3 = 99
99 ÷ 3 = 33
33 ÷ 3 = 11
11 ÷ 11 = 1
Result: 891 = 3 × 3 × 3 × 3 × 11 = 3⁴ × 11

The distinct prime factors of 891 are 3, 11. To factorize any other number, use the prime factorization calculator.

Factor tree of 891

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

Factor tree of 8918913297399333311
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 891

Number of factors10
Sum of factors1452
Sum of proper factors561
Prime factorization3⁴ × 11
Prime or composite?Composite
Even or odd?Odd
Perfect square?No
Perfect cube?No
ClassificationDeficient

What makes 891 interesting

  • 891 is a composite number, meaning it has more than two factors. It can be written as a product of smaller whole numbers in 5 different ways.
  • 891 is a deficient number: its proper factors sum to 561, which is 330 less than 891 itself.

How to find the factors of 891 yourself

Divide 891 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 √891 ≈ 29.85, because every factor above that pairs with one below it.

891 ÷ 1 = 891 ✓
891 ÷ 3 = 297 ✓
891 ÷ 9 = 99 ✓
891 ÷ 11 = 81 ✓
891 ÷ 27 = 33 ✓

Reading both columns gives every factor: 1, 3, 9, 11, 27, 33, 81, 99, 297, 891. The factor calculator does this automatically for any number.

Numbers mathematically connected to 891.

Frequently asked questions about 891

What are the factors of 891?

The factors of 891 are 1, 3, 9, 11, 27, 33, 81, 99, 297, and 891. That is 10 factors in total, counting both 1 and 891.

Is 891 a prime number?

No, 891 is not prime — it is a composite number with 10 factors. A prime number has exactly two factors, but 891 is also divisible by 3.

What is the prime factorization of 891?

The prime factorization of 891 is 3⁴ × 11. Written out in full: 3 × 3 × 3 × 3 × 11 = 891. Its distinct prime factors are 3, 11.

What two numbers multiply to give 891?

There are 5 pairs of whole numbers that multiply to 891: 1 × 891, 3 × 297, 9 × 99, 11 × 81, 27 × 33.

What is the sum of the factors of 891?

Adding all the factors of 891 together gives 1452. Excluding 891 itself, the proper factors sum to 561.

Is 891 a perfect square?

No, 891 is not a perfect square. There is no whole number that multiplies by itself to give 891. The nearest perfect squares are 841 and 900.

What is the largest factor of 891 other than itself?

The largest factor of 891 apart from 891 itself is 297, since 891 ÷ 297 = 3.

How many factors does 891 have?

891 has 10 factors: 1, 3, 9, 11, 27, 33, 81, 99, 297, and 891. You can verify this from the prime factorization 3⁴ × 11: add 1 to each exponent and multiply, giving 5 × 2 = 10.

Explore more

Try another number in the factor calculator, break 891 down further with the prime factorization calculator, or compare 891 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.