Factor Calculator

Factors of 784

The factors of 784 are 1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 392, and 784. In total, 784 has 15 factors. Its prime factorization is 2⁴ × 7², and the sum of all its factors is 1767. 784 is also a perfect square, equal to 28 × 28.

All factors of 784

Here are all 15 factors of 784, listed from smallest to largest.

12478141628495698112196392784

Factor pairs of 784

These 8 pairs of whole numbers each multiply to give 784.

1 × 784 = 784
2 × 392 = 784
4 × 196 = 784
7 × 112 = 784
8 × 98 = 784
14 × 56 = 784
16 × 49 = 784
28 × 28 = 784

Notice the pair (28, 28) — because 784 is a perfect square, this pair uses the same number twice.

Prime factorization of 784

Dividing 784 by the smallest prime at each step gives its prime factorization:

784 ÷ 2 = 392
392 ÷ 2 = 196
196 ÷ 2 = 98
98 ÷ 2 = 49
49 ÷ 7 = 7
7 ÷ 7 = 1
Result: 784 = 2 × 2 × 2 × 2 × 7 × 7 = 2⁴ × 7²

The distinct prime factors of 784 are 2, 7. To factorize any other number, use the prime factorization calculator.

Factor tree of 784

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

Factor tree of 7847842392219629824977
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 784

Number of factors15
Sum of factors1767
Sum of proper factors983
Prime factorization2⁴ × 7²
Prime or composite?Composite
Even or odd?Even
Perfect square?Yes (28²)
Perfect cube?No
ClassificationAbundant

What makes 784 interesting

  • 784 is a composite number, meaning it has more than two factors. It can be written as a product of smaller whole numbers in 8 different ways.
  • 784 is a perfect square: 28 × 28 = 784. This is why it has an odd number of factors (15) — the pair (28, 28) counts only once.
  • 784 is an abundant number: its proper factors sum to 983, which is 199 more than 784 itself.

How to find the factors of 784 yourself

Divide 784 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 √78428.00, because every factor above that pairs with one below it.

784 ÷ 1 = 784
784 ÷ 2 = 392
784 ÷ 4 = 196
784 ÷ 7 = 112
784 ÷ 8 = 98
784 ÷ 14 = 56
784 ÷ 16 = 49
784 ÷ 28 = 28

Reading both columns gives every factor: 1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 392, 784. The factor calculator does this automatically for any number.

Frequently asked questions about 784

What are the factors of 784?

The factors of 784 are 1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 392, and 784. That is 15 factors in total, counting both 1 and 784.

Is 784 a prime number?

No, 784 is not prime — it is a composite number with 15 factors. A prime number has exactly two factors, but 784 is also divisible by 2.

What is the prime factorization of 784?

The prime factorization of 784 is 2⁴ × 7². Written out in full: 2 × 2 × 2 × 2 × 7 × 7 = 784. Its distinct prime factors are 2, 7.

What two numbers multiply to give 784?

There are 8 pairs of whole numbers that multiply to 784: 1 × 784, 2 × 392, 4 × 196, 7 × 112, 8 × 98, 14 × 56, 16 × 49, 28 × 28.

What is the sum of the factors of 784?

Adding all the factors of 784 together gives 1767. Excluding 784 itself, the proper factors sum to 983.

Is 784 a perfect square?

Yes, 784 is a perfect square. It equals 28 × 28. Perfect squares always have an odd number of factors — 784 has 15.

What is the largest factor of 784 other than itself?

The largest factor of 784 apart from 784 itself is 392, since 784 ÷ 392 = 2.

How many factors does 784 have?

784 has 15 factors: 1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 392, and 784. You can verify this from the prime factorization 2⁴ × 7²: add 1 to each exponent and multiply, giving 5 × 3 = 15.

Explore more

Try another number in the factor calculator, break 784 down further with the prime factorization calculator, or compare 784 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.