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Factors of 529

529 has 3 factors: 1, 23 and 529. Its prime factorization is 23².

Factor pairs of 529

Factor×FactorProduct
1×529529
23×23529

Negative pairs work too: (−1) × (−529), (−23) × (−23) = 529.

Number of factors
3
Factor pairs
2
Sum of factors
553
Prime or composite
Composite
Even or odd
Odd
Perfect square
Yes (23²)
Prime factorization 23²

How to find the factors of 529

Test every whole number from 1 up to the square root of 529 (√529 ≈ 23.000). Each number that divides evenly gives you two factors at once: the divisor and the quotient.

  • 529 ÷ 1 = 529 — so 1 and 529 are factors
  • 529 ÷ 2 = 264.5 — not a whole number
  • 529 ÷ 3 = 176.333 — not a whole number
  • 529 ÷ 4 = 132.25 — not a whole number
  • 529 ÷ 5 = 105.8 — not a whole number
  • 529 ÷ 6 = 88.167 — not a whole number
  • 529 ÷ 7 = 75.571 — not a whole number
  • 529 ÷ 8 = 66.125 — not a whole number
  • 529 ÷ 9 = 58.778 — not a whole number
  • 529 ÷ 10 = 52.9 — not a whole number
  • 529 ÷ 11 = 48.091 — not a whole number
  • 529 ÷ 12 = 44.083 — not a whole number
  • 529 ÷ 13 = 40.692 — not a whole number
  • 529 ÷ 14 = 37.786 — not a whole number
  • 529 ÷ 15 = 35.267 — not a whole number
  • 529 ÷ 16 = 33.063 — not a whole number
  • 529 ÷ 17 = 31.118 — not a whole number
  • 529 ÷ 18 = 29.389 — not a whole number
  • 529 ÷ 19 = 27.842 — not a whole number
  • 529 ÷ 20 = 26.45 — not a whole number
  • 529 ÷ 21 = 25.19 — not a whole number
  • 529 ÷ 22 = 24.045 — not a whole number
  • 529 ÷ 23 = 23 — so 23 and 23 are factors

Collecting both numbers from every successful division gives the complete list: 1, 23 and 529.

Prime factorization of 529

Divide by the smallest prime that fits, and keep going until the quotient is 1:

529 ÷ 23 = 23
23 ÷ 23 = 1

The primes you divided by give 529 = 23². From the exponents you can also count the factors without listing them: (2 + 1) = 3.

Properties of 529

  • 529 is a composite number.
  • The sum of all its factors is 553; the sum of its proper factors (excluding 529) is 24, which makes it a deficient number (its proper factors add up to less than itself).
  • 529 is a perfect square: 23 × 23. Perfect squares always have an odd number of factors.
  • Multiples of 529 include 1,058, 1,587, 2,116, 2,645 and so on.

Factors vs. multiples

Factors of 529 are the numbers that divide into it; multiples of 529 are the numbers it divides into. Every number has a limited set of factors but infinitely many multiples. To work with any other number, use the factors calculator, or find shared factors with the GCF calculator.

Frequently asked questions

What are the factors of 529?

The factors of 529 are 1, 23 and 529. Each of these divides 529 with no remainder.

How many factors does 529 have?

529 has 3 positive factors, which form 2 factor pairs. Counting negative factors as well doubles that to 6.

What is the prime factorization of 529?

529 = 23². Its distinct prime factors are 23.

Is 529 a prime number?

No. 529 is composite because it has 3 factors, more than the two a prime number has.