Factor Calculator

Factors of 828

The factors of 828 are 1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276, 414, and 828. In total, 828 has 18 factors. Its prime factorization is 2² × 3² × 23, and the sum of all its factors is 2184.

All factors of 828

Here are all 18 factors of 828, listed from smallest to largest.

12346912182336466992138207276414828

Factor pairs of 828

These 9 pairs of whole numbers each multiply to give 828.

1 × 828 = 828
2 × 414 = 828
3 × 276 = 828
4 × 207 = 828
6 × 138 = 828
9 × 92 = 828
12 × 69 = 828
18 × 46 = 828
23 × 36 = 828

Prime factorization of 828

Dividing 828 by the smallest prime at each step gives its prime factorization:

828 ÷ 2 = 414
414 ÷ 2 = 207
207 ÷ 3 = 69
69 ÷ 3 = 23
23 ÷ 23 = 1
Result: 828 = 2 × 2 × 3 × 3 × 23 = 2² × 3² × 23

The distinct prime factors of 828 are 2, 3, 23. To factorize any other number, use the prime factorization calculator.

Factor tree of 828

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

Factor tree of 82882824142207369323
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 828

Number of factors18
Sum of factors2184
Sum of proper factors1356
Prime factorization2² × 3² × 23
Prime or composite?Composite
Even or odd?Even
Perfect square?No
Perfect cube?No
ClassificationAbundant

What makes 828 interesting

  • 828 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.
  • 828 is an abundant number: its proper factors sum to 1356, which is 528 more than 828 itself.
  • 828 has 3 distinct prime factors (2, 3, 23), which is why it has so many divisors.

How to find the factors of 828 yourself

Divide 828 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 √82828.77, because every factor above that pairs with one below it.

828 ÷ 1 = 828
828 ÷ 2 = 414
828 ÷ 3 = 276
828 ÷ 4 = 207
828 ÷ 6 = 138
828 ÷ 9 = 92
828 ÷ 12 = 69
828 ÷ 18 = 46
828 ÷ 23 = 36

Reading both columns gives every factor: 1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276, 414, 828. The factor calculator does this automatically for any number.

Frequently asked questions about 828

What are the factors of 828?

The factors of 828 are 1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276, 414, and 828. That is 18 factors in total, counting both 1 and 828.

Is 828 a prime number?

No, 828 is not prime — it is a composite number with 18 factors. A prime number has exactly two factors, but 828 is also divisible by 2.

What is the prime factorization of 828?

The prime factorization of 828 is 2² × 3² × 23. Written out in full: 2 × 2 × 3 × 3 × 23 = 828. Its distinct prime factors are 2, 3, 23.

What two numbers multiply to give 828?

There are 9 pairs of whole numbers that multiply to 828: 1 × 828, 2 × 414, 3 × 276, 4 × 207, 6 × 138, 9 × 92, 12 × 69, 18 × 46, 23 × 36.

What is the sum of the factors of 828?

Adding all the factors of 828 together gives 2184. Excluding 828 itself, the proper factors sum to 1356.

Is 828 a perfect square?

No, 828 is not a perfect square. There is no whole number that multiplies by itself to give 828. The nearest perfect squares are 784 and 841.

What is the largest factor of 828 other than itself?

The largest factor of 828 apart from 828 itself is 414, since 828 ÷ 414 = 2.

How many factors does 828 have?

828 has 18 factors: 1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276, 414, and 828. You can verify this from the prime factorization 2² × 3² × 23: add 1 to each exponent and multiply, giving 3 × 3 × 2 = 18.

Explore more

Try another number in the factor calculator, break 828 down further with the prime factorization calculator, or compare 828 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.