Factor Calculator

Factors of 648

The factors of 648 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 324, and 648. In total, 648 has 20 factors. Its prime factorization is 2³ × 3⁴, and the sum of all its factors is 1815.

All factors of 648

Here are all 20 factors of 648, listed from smallest to largest.

12346891218242736547281108162216324648

Factor pairs of 648

These 10 pairs of whole numbers each multiply to give 648.

1 × 648 = 648
2 × 324 = 648
3 × 216 = 648
4 × 162 = 648
6 × 108 = 648
8 × 81 = 648
9 × 72 = 648
12 × 54 = 648
18 × 36 = 648
24 × 27 = 648

Prime factorization of 648

Dividing 648 by the smallest prime at each step gives its prime factorization:

648 ÷ 2 = 324
324 ÷ 2 = 162
162 ÷ 2 = 81
81 ÷ 3 = 27
27 ÷ 3 = 9
9 ÷ 3 = 3
3 ÷ 3 = 1
Result: 648 = 2 × 2 × 2 × 3 × 3 × 3 × 3 = 2³ × 3⁴

The distinct prime factors of 648 are 2, 3. To factorize any other number, use the prime factorization calculator.

Factor tree of 648

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

Factor tree of 648648232421622813273933
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 648

Number of factors20
Sum of factors1815
Sum of proper factors1167
Prime factorization2³ × 3⁴
Prime or composite?Composite
Even or odd?Even
Perfect square?No
Perfect cube?No
ClassificationAbundant

What makes 648 interesting

  • 648 is a composite number, meaning it has more than two factors. It can be written as a product of smaller whole numbers in 10 different ways.
  • 648 is an abundant number: its proper factors sum to 1167, which is 519 more than 648 itself.

How to find the factors of 648 yourself

Divide 648 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 √64825.46, because every factor above that pairs with one below it.

648 ÷ 1 = 648
648 ÷ 2 = 324
648 ÷ 3 = 216
648 ÷ 4 = 162
648 ÷ 6 = 108
648 ÷ 8 = 81
648 ÷ 9 = 72
648 ÷ 12 = 54
648 ÷ 18 = 36
648 ÷ 24 = 27

Reading both columns gives every factor: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 324, 648. The factor calculator does this automatically for any number.

Frequently asked questions about 648

What are the factors of 648?

The factors of 648 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 324, and 648. That is 20 factors in total, counting both 1 and 648.

Is 648 a prime number?

No, 648 is not prime — it is a composite number with 20 factors. A prime number has exactly two factors, but 648 is also divisible by 2.

What is the prime factorization of 648?

The prime factorization of 648 is 2³ × 3⁴. Written out in full: 2 × 2 × 2 × 3 × 3 × 3 × 3 = 648. Its distinct prime factors are 2, 3.

What two numbers multiply to give 648?

There are 10 pairs of whole numbers that multiply to 648: 1 × 648, 2 × 324, 3 × 216, 4 × 162, 6 × 108, 8 × 81, 9 × 72, 12 × 54, 18 × 36, 24 × 27.

What is the sum of the factors of 648?

Adding all the factors of 648 together gives 1815. Excluding 648 itself, the proper factors sum to 1167.

Is 648 a perfect square?

No, 648 is not a perfect square. There is no whole number that multiplies by itself to give 648. The nearest perfect squares are 625 and 676.

What is the largest factor of 648 other than itself?

The largest factor of 648 apart from 648 itself is 324, since 648 ÷ 324 = 2.

How many factors does 648 have?

648 has 20 factors: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 324, and 648. You can verify this from the prime factorization 2³ × 3⁴: add 1 to each exponent and multiply, giving 4 × 5 = 20.

Explore more

Try another number in the factor calculator, break 648 down further with the prime factorization calculator, or compare 648 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.