Factor Calculator

Factors of 529

The factors of 529 are 1, 23, and 529. In total, 529 has 3 factors. Its prime factorization is 23², and the sum of all its factors is 553. 529 is also a perfect square, equal to 23 × 23.

All factors of 529

Here are all 3 factors of 529, listed from smallest to largest.

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Factor pairs of 529

These 2 pairs of whole numbers each multiply to give 529.

1 × 529 = 529
23 × 23 = 529

Notice the pair (23, 23) — because 529 is a perfect square, this pair uses the same number twice.

Prime factorization of 529

Dividing 529 by the smallest prime at each step gives its prime factorization:

529 ÷ 23 = 23
23 ÷ 23 = 1
Result: 529 = 23 × 23 = 23²

The distinct prime factors of 529 are 23. To factorize any other number, use the prime factorization calculator.

Factor tree of 529

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

Factor tree of 5295292323
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 529

Number of factors3
Sum of factors553
Sum of proper factors24
Prime factorization23²
Prime or composite?Composite
Even or odd?Odd
Perfect square?Yes (23²)
Perfect cube?No
ClassificationDeficient

What makes 529 interesting

  • 529 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.
  • 529 is a perfect square: 23 × 23 = 529. This is why it has an odd number of factors (3) — the pair (23, 23) counts only once.
  • 529 is a deficient number: its proper factors sum to 24, which is 505 less than 529 itself.
  • 529 is a prime power: it is 23 raised to the power of 2. All of its factors are powers of 23.

How to find the factors of 529 yourself

Divide 529 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 √529 ≈ 23.00, because every factor above that pairs with one below it.

529 ÷ 1 = 529 ✓
529 ÷ 23 = 23 ✓

Reading both columns gives every factor: 1, 23, 529. The factor calculator does this automatically for any number.

Numbers mathematically connected to 529.

Frequently asked questions about 529

What are the factors of 529?

The factors of 529 are 1, 23, and 529. That is 3 factors in total, counting both 1 and 529.

Is 529 a prime number?

No, 529 is not prime — it is a composite number with 3 factors. A prime number has exactly two factors, but 529 is also divisible by 23.

What is the prime factorization of 529?

The prime factorization of 529 is 23². Written out in full: 23 × 23 = 529. Its distinct prime factors are 23.

What two numbers multiply to give 529?

There are 2 pairs of whole numbers that multiply to 529: 1 × 529, 23 × 23.

What is the sum of the factors of 529?

Adding all the factors of 529 together gives 553. Excluding 529 itself, the proper factors sum to 24.

Is 529 a perfect square?

Yes, 529 is a perfect square. It equals 23 × 23. Perfect squares always have an odd number of factors — 529 has 3.

What is the largest factor of 529 other than itself?

The largest factor of 529 apart from 529 itself is 23, since 529 ÷ 23 = 23.

How many factors does 529 have?

529 has 3 factors: 1, 23, and 529. You can verify this from the prime factorization 23²: add 1 to each exponent and multiply, giving 3 = 3.

Explore more

Try another number in the factor calculator, break 529 down further with the prime factorization calculator, or compare 529 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.