Factor Calculator

Factors of 522

The factors of 522 are 1, 2, 3, 6, 9, 18, 29, 58, 87, 174, 261, and 522. In total, 522 has 12 factors. Its prime factorization is 2 × 3² × 29, and the sum of all its factors is 1170.

All factors of 522

Here are all 12 factors of 522, listed from smallest to largest.

1236918295887174261522

Factor pairs of 522

These 6 pairs of whole numbers each multiply to give 522.

1 × 522 = 522
2 × 261 = 522
3 × 174 = 522
6 × 87 = 522
9 × 58 = 522
18 × 29 = 522

Prime factorization of 522

Dividing 522 by the smallest prime at each step gives its prime factorization:

522 ÷ 2 = 261
261 ÷ 3 = 87
87 ÷ 3 = 29
29 ÷ 29 = 1
Result: 522 = 2 × 3 × 3 × 29 = 2 × 3² × 29

The distinct prime factors of 522 are 2, 3, 29. To factorize any other number, use the prime factorization calculator.

Factor tree of 522

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

Factor tree of 5225222261387329
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 522

Number of factors12
Sum of factors1170
Sum of proper factors648
Prime factorization2 × 3² × 29
Prime or composite?Composite
Even or odd?Even
Perfect square?No
Perfect cube?No
ClassificationAbundant

What makes 522 interesting

  • 522 is a composite number, meaning it has more than two factors. It can be written as a product of smaller whole numbers in 6 different ways.
  • 522 is an abundant number: its proper factors sum to 648, which is 126 more than 522 itself.
  • 522 has 3 distinct prime factors (2, 3, 29), which is why it has so many divisors.

How to find the factors of 522 yourself

Divide 522 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 √522 ≈ 22.85, because every factor above that pairs with one below it.

522 ÷ 1 = 522 ✓
522 ÷ 2 = 261 ✓
522 ÷ 3 = 174 ✓
522 ÷ 6 = 87 ✓
522 ÷ 9 = 58 ✓
522 ÷ 18 = 29 ✓

Reading both columns gives every factor: 1, 2, 3, 6, 9, 18, 29, 58, 87, 174, 261, 522. The factor calculator does this automatically for any number.

Numbers mathematically connected to 522.

Frequently asked questions about 522

What are the factors of 522?

The factors of 522 are 1, 2, 3, 6, 9, 18, 29, 58, 87, 174, 261, and 522. That is 12 factors in total, counting both 1 and 522.

Is 522 a prime number?

No, 522 is not prime — it is a composite number with 12 factors. A prime number has exactly two factors, but 522 is also divisible by 2.

What is the prime factorization of 522?

The prime factorization of 522 is 2 × 3² × 29. Written out in full: 2 × 3 × 3 × 29 = 522. Its distinct prime factors are 2, 3, 29.

What two numbers multiply to give 522?

There are 6 pairs of whole numbers that multiply to 522: 1 × 522, 2 × 261, 3 × 174, 6 × 87, 9 × 58, 18 × 29.

What is the sum of the factors of 522?

Adding all the factors of 522 together gives 1170. Excluding 522 itself, the proper factors sum to 648.

Is 522 a perfect square?

No, 522 is not a perfect square. There is no whole number that multiplies by itself to give 522. The nearest perfect squares are 484 and 529.

What is the largest factor of 522 other than itself?

The largest factor of 522 apart from 522 itself is 261, since 522 ÷ 261 = 2.

How many factors does 522 have?

522 has 12 factors: 1, 2, 3, 6, 9, 18, 29, 58, 87, 174, 261, and 522. You can verify this from the prime factorization 2 × 3² × 29: add 1 to each exponent and multiply, giving 2 × 3 × 2 = 12.

Explore more

Try another number in the factor calculator, break 522 down further with the prime factorization calculator, or compare 522 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.