Factors of 400
The factors of 400 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, and 400. In total, 400 has 15 factors. Its prime factorization is 2⁴ × 5², and the sum of all its factors is 961. 400 is also a perfect square, equal to 20 × 20.
All factors of 400
Here are all 15 factors of 400, listed from smallest to largest.
Factor pairs of 400
These 8 pairs of whole numbers each multiply to give 400.
Notice the pair (20, 20) — because 400 is a perfect square, this pair uses the same number twice.
Prime factorization of 400
Dividing 400 by the smallest prime at each step gives its prime factorization:
The distinct prime factors of 400 are 2, 5. To factorize any other number, use the prime factorization calculator.
Factor tree of 400
A factor tree shows the same prime factorization visually. Each composite branch splits until every endpoint is a prime number.
Properties of 400
| Number of factors | 15 |
|---|---|
| Sum of factors | 961 |
| Sum of proper factors | 561 |
| Prime factorization | 2⁴ × 5² |
| Prime or composite? | Composite |
| Even or odd? | Even |
| Perfect square? | Yes (20²) |
| Perfect cube? | No |
| Classification | Abundant |
What makes 400 interesting
- 400 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.
- 400 is a perfect square: 20 × 20 = 400. This is why it has an odd number of factors (15) — the pair (20, 20) counts only once.
- 400 is an abundant number: its proper factors sum to 561, which is 161 more than 400 itself.
How to find the factors of 400 yourself
Divide 400 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 √400 ≈ 20.00, because every factor above that pairs with one below it.
Reading both columns gives every factor: 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400. The factor calculator does this automatically for any number.
Related numbers
Numbers mathematically connected to 400.
Frequently asked questions about 400
What are the factors of 400?
Is 400 a prime number?
What is the prime factorization of 400?
What two numbers multiply to give 400?
What is the sum of the factors of 400?
Is 400 a perfect square?
What is the largest factor of 400 other than itself?
How many factors does 400 have?
Explore more
Try another number in the factor calculator, break 400 down further with the prime factorization calculator, or compare 400 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.