Factor Calculator

Factors of 213

The factors of 213 are 1, 3, 71, and 213. In total, 213 has 4 factors. Its prime factorization is 3 × 71, and the sum of all its factors is 288.

All factors of 213

Here are all 4 factors of 213, listed from smallest to largest.

1371213

Factor pairs of 213

These 2 pairs of whole numbers each multiply to give 213.

1 × 213 = 213
3 × 71 = 213

Prime factorization of 213

Dividing 213 by the smallest prime at each step gives its prime factorization:

213 ÷ 3 = 71
71 ÷ 71 = 1
Result: 213 = 3 × 71 = 3 × 71

The distinct prime factors of 213 are 3, 71. To factorize any other number, use the prime factorization calculator.

Factor tree of 213

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

Factor tree of 213213371
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 213

Number of factors4
Sum of factors288
Sum of proper factors75
Prime factorization3 × 71
Prime or composite?Composite
Even or odd?Odd
Perfect square?No
Perfect cube?No
ClassificationDeficient

What makes 213 interesting

  • 213 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.
  • 213 is a deficient number: its proper factors sum to 75, which is 138 less than 213 itself.

How to find the factors of 213 yourself

Divide 213 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 √213 ≈ 14.59, because every factor above that pairs with one below it.

213 ÷ 1 = 213 ✓
213 ÷ 3 = 71 ✓

Reading both columns gives every factor: 1, 3, 71, 213. The factor calculator does this automatically for any number.

Numbers mathematically connected to 213.

Frequently asked questions about 213

What are the factors of 213?

The factors of 213 are 1, 3, 71, and 213. That is 4 factors in total, counting both 1 and 213.

Is 213 a prime number?

No, 213 is not prime — it is a composite number with 4 factors. A prime number has exactly two factors, but 213 is also divisible by 3.

What is the prime factorization of 213?

The prime factorization of 213 is 3 × 71. Written out in full: 3 × 71 = 213. Its distinct prime factors are 3, 71.

What two numbers multiply to give 213?

There are 2 pairs of whole numbers that multiply to 213: 1 × 213, 3 × 71.

What is the sum of the factors of 213?

Adding all the factors of 213 together gives 288. Excluding 213 itself, the proper factors sum to 75.

Is 213 a perfect square?

No, 213 is not a perfect square. There is no whole number that multiplies by itself to give 213. The nearest perfect squares are 196 and 225.

What is the largest factor of 213 other than itself?

The largest factor of 213 apart from 213 itself is 71, since 213 ÷ 71 = 3.

How many factors does 213 have?

213 has 4 factors: 1, 3, 71, and 213. You can verify this from the prime factorization 3 × 71: add 1 to each exponent and multiply, giving 2 × 2 = 4.

Explore more

Try another number in the factor calculator, break 213 down further with the prime factorization calculator, or compare 213 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.