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.
Factor pairs of 784
These 8 pairs of whole numbers each multiply to give 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:
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.
Properties of 784
| Number of factors | 15 |
|---|---|
| Sum of factors | 1767 |
| Sum of proper factors | 983 |
| Prime factorization | 2⁴ × 7² |
| Prime or composite? | Composite |
| Even or odd? | Even |
| Perfect square? | Yes (28²) |
| Perfect cube? | No |
| Classification | Abundant |
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 √784 ≈ 28.00, because every factor above that pairs with one below it.
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.
Related numbers
Numbers mathematically connected to 784.
Frequently asked questions about 784
What are the factors of 784?
Is 784 a prime number?
What is the prime factorization of 784?
What two numbers multiply to give 784?
What is the sum of the factors of 784?
Is 784 a perfect square?
What is the largest factor of 784 other than itself?
How many factors does 784 have?
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.