Factor Calculator

Factors of 504

The factors of 504 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252, and 504. In total, 504 has 24 factors. Its prime factorization is 2³ × 3² × 7, and the sum of all its factors is 1560.

All factors of 504

Here are all 24 factors of 504, listed from smallest to largest.

12346789121418212428364256637284126168252504

Factor pairs of 504

These 12 pairs of whole numbers each multiply to give 504.

1 × 504 = 504
2 × 252 = 504
3 × 168 = 504
4 × 126 = 504
6 × 84 = 504
7 × 72 = 504
8 × 63 = 504
9 × 56 = 504
12 × 42 = 504
14 × 36 = 504
18 × 28 = 504
21 × 24 = 504

Prime factorization of 504

Dividing 504 by the smallest prime at each step gives its prime factorization:

504 ÷ 2 = 252
252 ÷ 2 = 126
126 ÷ 2 = 63
63 ÷ 3 = 21
21 ÷ 3 = 7
7 ÷ 7 = 1
Result: 504 = 2 × 2 × 2 × 3 × 3 × 7 = 2³ × 3² × 7

The distinct prime factors of 504 are 2, 3, 7. To factorize any other number, use the prime factorization calculator.

Factor tree of 504

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

Factor tree of 5045042252212626332137
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 504

Number of factors24
Sum of factors1560
Sum of proper factors1056
Prime factorization2³ × 3² × 7
Prime or composite?Composite
Even or odd?Even
Perfect square?No
Perfect cube?No
ClassificationAbundant

What makes 504 interesting

  • 504 is a composite number, meaning it has more than two factors. It can be written as a product of smaller whole numbers in 12 different ways.
  • 504 is an abundant number: its proper factors sum to 1056, which is 552 more than 504 itself.
  • 504 has 3 distinct prime factors (2, 3, 7), which is why it has so many divisors.

How to find the factors of 504 yourself

Divide 504 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 √50422.45, because every factor above that pairs with one below it.

504 ÷ 1 = 504
504 ÷ 2 = 252
504 ÷ 3 = 168
504 ÷ 4 = 126
504 ÷ 6 = 84
504 ÷ 7 = 72
504 ÷ 8 = 63
504 ÷ 9 = 56
504 ÷ 12 = 42
504 ÷ 14 = 36
504 ÷ 18 = 28
504 ÷ 21 = 24

Reading both columns gives every factor: 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252, 504. The factor calculator does this automatically for any number.

Frequently asked questions about 504

What are the factors of 504?

The factors of 504 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252, and 504. That is 24 factors in total, counting both 1 and 504.

Is 504 a prime number?

No, 504 is not prime — it is a composite number with 24 factors. A prime number has exactly two factors, but 504 is also divisible by 2.

What is the prime factorization of 504?

The prime factorization of 504 is 2³ × 3² × 7. Written out in full: 2 × 2 × 2 × 3 × 3 × 7 = 504. Its distinct prime factors are 2, 3, 7.

What two numbers multiply to give 504?

There are 12 pairs of whole numbers that multiply to 504: 1 × 504, 2 × 252, 3 × 168, 4 × 126, 6 × 84, 7 × 72, 8 × 63, 9 × 56, 12 × 42, 14 × 36, 18 × 28, 21 × 24.

What is the sum of the factors of 504?

Adding all the factors of 504 together gives 1560. Excluding 504 itself, the proper factors sum to 1056.

Is 504 a perfect square?

No, 504 is not a perfect square. There is no whole number that multiplies by itself to give 504. The nearest perfect squares are 484 and 529.

What is the largest factor of 504 other than itself?

The largest factor of 504 apart from 504 itself is 252, since 504 ÷ 252 = 2.

How many factors does 504 have?

504 has 24 factors: 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 168, 252, and 504. You can verify this from the prime factorization 2³ × 3² × 7: add 1 to each exponent and multiply, giving 4 × 3 × 2 = 24.

Explore more

Try another number in the factor calculator, break 504 down further with the prime factorization calculator, or compare 504 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.