Factor Calculator

Factors of 217

The factors of 217 are 1, 7, 31, and 217. In total, 217 has 4 factors. Its prime factorization is 7 × 31, and the sum of all its factors is 256.

All factors of 217

Here are all 4 factors of 217, listed from smallest to largest.

1731217

Factor pairs of 217

These 2 pairs of whole numbers each multiply to give 217.

1 × 217 = 217
7 × 31 = 217

Prime factorization of 217

Dividing 217 by the smallest prime at each step gives its prime factorization:

217 ÷ 7 = 31
31 ÷ 31 = 1
Result: 217 = 7 × 31 = 7 × 31

The distinct prime factors of 217 are 7, 31. To factorize any other number, use the prime factorization calculator.

Factor tree of 217

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

Factor tree of 217217731
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 217

Number of factors4
Sum of factors256
Sum of proper factors39
Prime factorization7 × 31
Prime or composite?Composite
Even or odd?Odd
Perfect square?No
Perfect cube?No
ClassificationDeficient

What makes 217 interesting

  • 217 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.
  • 217 is a deficient number: its proper factors sum to 39, which is 178 less than 217 itself.

How to find the factors of 217 yourself

Divide 217 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 √21714.73, because every factor above that pairs with one below it.

217 ÷ 1 = 217
217 ÷ 7 = 31

Reading both columns gives every factor: 1, 7, 31, 217. The factor calculator does this automatically for any number.

Frequently asked questions about 217

What are the factors of 217?

The factors of 217 are 1, 7, 31, and 217. That is 4 factors in total, counting both 1 and 217.

Is 217 a prime number?

No, 217 is not prime — it is a composite number with 4 factors. A prime number has exactly two factors, but 217 is also divisible by 7.

What is the prime factorization of 217?

The prime factorization of 217 is 7 × 31. Written out in full: 7 × 31 = 217. Its distinct prime factors are 7, 31.

What two numbers multiply to give 217?

There are 2 pairs of whole numbers that multiply to 217: 1 × 217, 7 × 31.

What is the sum of the factors of 217?

Adding all the factors of 217 together gives 256. Excluding 217 itself, the proper factors sum to 39.

Is 217 a perfect square?

No, 217 is not a perfect square. There is no whole number that multiplies by itself to give 217. The nearest perfect squares are 196 and 225.

What is the largest factor of 217 other than itself?

The largest factor of 217 apart from 217 itself is 31, since 217 ÷ 31 = 7.

How many factors does 217 have?

217 has 4 factors: 1, 7, 31, and 217. You can verify this from the prime factorization 7 × 31: add 1 to each exponent and multiply, giving 2 × 2 = 4.

Explore more

Try another number in the factor calculator, break 217 down further with the prime factorization calculator, or compare 217 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.