Factor Calculator

Factors of 91

The factors of 91 are 1, 7, 13, and 91. In total, 91 has 4 factors. Its prime factorization is 7 × 13, and the sum of all its factors is 112.

All factors of 91

Here are all 4 factors of 91, listed from smallest to largest.

171391

Factor pairs of 91

These 2 pairs of whole numbers each multiply to give 91.

1 × 91 = 91
7 × 13 = 91

Prime factorization of 91

Dividing 91 by the smallest prime at each step gives its prime factorization:

91 ÷ 7 = 13
13 ÷ 13 = 1
Result: 91 = 7 × 13 = 7 × 13

The distinct prime factors of 91 are 7, 13. To factorize any other number, use the prime factorization calculator.

Factor tree of 91

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

Factor tree of 9191713
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 91

Number of factors4
Sum of factors112
Sum of proper factors21
Prime factorization7 × 13
Prime or composite?Composite
Even or odd?Odd
Perfect square?No
Perfect cube?No
ClassificationDeficient

What makes 91 interesting

  • 91 is a composite number, meaning it has more than two factors. It can be written as a product of smaller whole numbers in 2 different ways.
  • 91 is a deficient number: its proper factors sum to 21, which is 70 less than 91 itself.
  • 91 is a triangular number — it is the sum of the first 13 whole numbers (1 + 2 + … + 13 = 91).

How to find the factors of 91 yourself

Divide 91 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 √919.54, because every factor above that pairs with one below it.

91 ÷ 1 = 91
91 ÷ 7 = 13

Reading both columns gives every factor: 1, 7, 13, 91. The factor calculator does this automatically for any number.

Frequently asked questions about 91

What are the factors of 91?

The factors of 91 are 1, 7, 13, and 91. That is 4 factors in total, counting both 1 and 91.

Is 91 a prime number?

No, 91 is not prime — it is a composite number with 4 factors. A prime number has exactly two factors, but 91 is also divisible by 7.

What is the prime factorization of 91?

The prime factorization of 91 is 7 × 13. Written out in full: 7 × 13 = 91. Its distinct prime factors are 7, 13.

What two numbers multiply to give 91?

There are 2 pairs of whole numbers that multiply to 91: 1 × 91, 7 × 13.

What is the sum of the factors of 91?

Adding all the factors of 91 together gives 112. Excluding 91 itself, the proper factors sum to 21.

Is 91 a perfect square?

No, 91 is not a perfect square. There is no whole number that multiplies by itself to give 91. The nearest perfect squares are 81 and 100.

What is the largest factor of 91 other than itself?

The largest factor of 91 apart from 91 itself is 13, since 91 ÷ 13 = 7.

How many factors does 91 have?

91 has 4 factors: 1, 7, 13, and 91. You can verify this from the prime factorization 7 × 13: add 1 to each exponent and multiply, giving 2 × 2 = 4.

Explore more

Try another number in the factor calculator, break 91 down further with the prime factorization calculator, or compare 91 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.