Factors of 441
The factors of 441 are 1, 3, 7, 9, 21, 49, 63, 147, and 441. In total, 441 has 9 factors. Its prime factorization is 3² × 7², and the sum of all its factors is 741. 441 is also a perfect square, equal to 21 × 21.
All factors of 441
Here are all 9 factors of 441, listed from smallest to largest.
Factor pairs of 441
These 5 pairs of whole numbers each multiply to give 441.
Notice the pair (21, 21) — because 441 is a perfect square, this pair uses the same number twice.
Prime factorization of 441
Dividing 441 by the smallest prime at each step gives its prime factorization:
The distinct prime factors of 441 are 3, 7. To factorize any other number, use the prime factorization calculator.
Factor tree of 441
A factor tree shows the same prime factorization visually. Each composite branch splits until every endpoint is a prime number.
Properties of 441
| Number of factors | 9 |
|---|---|
| Sum of factors | 741 |
| Sum of proper factors | 300 |
| Prime factorization | 3² × 7² |
| Prime or composite? | Composite |
| Even or odd? | Odd |
| Perfect square? | Yes (21²) |
| Perfect cube? | No |
| Classification | Deficient |
What makes 441 interesting
- 441 is a composite number, meaning it has more than two factors. It can be written as a product of smaller whole numbers in 5 different ways.
- 441 is a perfect square: 21 × 21 = 441. This is why it has an odd number of factors (9) — the pair (21, 21) counts only once.
- 441 is a deficient number: its proper factors sum to 300, which is 141 less than 441 itself.
How to find the factors of 441 yourself
Divide 441 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 √441 ≈ 21.00, because every factor above that pairs with one below it.
Reading both columns gives every factor: 1, 3, 7, 9, 21, 49, 63, 147, 441. The factor calculator does this automatically for any number.
Related numbers
Numbers mathematically connected to 441.
Frequently asked questions about 441
What are the factors of 441?
Is 441 a prime number?
What is the prime factorization of 441?
What two numbers multiply to give 441?
What is the sum of the factors of 441?
Is 441 a perfect square?
What is the largest factor of 441 other than itself?
How many factors does 441 have?
Explore more
Try another number in the factor calculator, break 441 down further with the prime factorization calculator, or compare 441 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.