Factor Calculator

Factors of 684

The factors of 684 are 1, 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, 342, and 684. In total, 684 has 18 factors. Its prime factorization is 2² × 3² × 19, and the sum of all its factors is 1820.

All factors of 684

Here are all 18 factors of 684, listed from smallest to largest.

12346912181936385776114171228342684

Factor pairs of 684

These 9 pairs of whole numbers each multiply to give 684.

1 × 684 = 684
2 × 342 = 684
3 × 228 = 684
4 × 171 = 684
6 × 114 = 684
9 × 76 = 684
12 × 57 = 684
18 × 38 = 684
19 × 36 = 684

Prime factorization of 684

Dividing 684 by the smallest prime at each step gives its prime factorization:

684 ÷ 2 = 342
342 ÷ 2 = 171
171 ÷ 3 = 57
57 ÷ 3 = 19
19 ÷ 19 = 1
Result: 684 = 2 × 2 × 3 × 3 × 19 = 2² × 3² × 19

The distinct prime factors of 684 are 2, 3, 19. To factorize any other number, use the prime factorization calculator.

Factor tree of 684

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

Factor tree of 68468423422171357319
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 684

Number of factors18
Sum of factors1820
Sum of proper factors1136
Prime factorization2² × 3² × 19
Prime or composite?Composite
Even or odd?Even
Perfect square?No
Perfect cube?No
ClassificationAbundant

What makes 684 interesting

  • 684 is a composite number, meaning it has more than two factors. It can be written as a product of smaller whole numbers in 9 different ways.
  • 684 is an abundant number: its proper factors sum to 1136, which is 452 more than 684 itself.
  • 684 has 3 distinct prime factors (2, 3, 19), which is why it has so many divisors.

How to find the factors of 684 yourself

Divide 684 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 √68426.15, because every factor above that pairs with one below it.

684 ÷ 1 = 684
684 ÷ 2 = 342
684 ÷ 3 = 228
684 ÷ 4 = 171
684 ÷ 6 = 114
684 ÷ 9 = 76
684 ÷ 12 = 57
684 ÷ 18 = 38
684 ÷ 19 = 36

Reading both columns gives every factor: 1, 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, 342, 684. The factor calculator does this automatically for any number.

Frequently asked questions about 684

What are the factors of 684?

The factors of 684 are 1, 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, 342, and 684. That is 18 factors in total, counting both 1 and 684.

Is 684 a prime number?

No, 684 is not prime — it is a composite number with 18 factors. A prime number has exactly two factors, but 684 is also divisible by 2.

What is the prime factorization of 684?

The prime factorization of 684 is 2² × 3² × 19. Written out in full: 2 × 2 × 3 × 3 × 19 = 684. Its distinct prime factors are 2, 3, 19.

What two numbers multiply to give 684?

There are 9 pairs of whole numbers that multiply to 684: 1 × 684, 2 × 342, 3 × 228, 4 × 171, 6 × 114, 9 × 76, 12 × 57, 18 × 38, 19 × 36.

What is the sum of the factors of 684?

Adding all the factors of 684 together gives 1820. Excluding 684 itself, the proper factors sum to 1136.

Is 684 a perfect square?

No, 684 is not a perfect square. There is no whole number that multiplies by itself to give 684. The nearest perfect squares are 676 and 729.

What is the largest factor of 684 other than itself?

The largest factor of 684 apart from 684 itself is 342, since 684 ÷ 342 = 2.

How many factors does 684 have?

684 has 18 factors: 1, 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, 342, and 684. You can verify this from the prime factorization 2² × 3² × 19: add 1 to each exponent and multiply, giving 3 × 3 × 2 = 18.

Explore more

Try another number in the factor calculator, break 684 down further with the prime factorization calculator, or compare 684 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.