Factor Calculator

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.

1379214963147441

Factor pairs of 441

These 5 pairs of whole numbers each multiply to give 441.

1 × 441 = 441
3 × 147 = 441
7 × 63 = 441
9 × 49 = 441
21 × 21 = 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:

441 ÷ 3 = 147
147 ÷ 3 = 49
49 ÷ 7 = 7
7 ÷ 7 = 1
Result: 441 = 3 × 3 × 7 × 7 = 3² × 7²

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.

Factor tree of 441441314734977
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 441

Number of factors9
Sum of factors741
Sum of proper factors300
Prime factorization3² × 7²
Prime or composite?Composite
Even or odd?Odd
Perfect square?Yes (21²)
Perfect cube?No
ClassificationDeficient

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 √44121.00, because every factor above that pairs with one below it.

441 ÷ 1 = 441
441 ÷ 3 = 147
441 ÷ 7 = 63
441 ÷ 9 = 49
441 ÷ 21 = 21

Reading both columns gives every factor: 1, 3, 7, 9, 21, 49, 63, 147, 441. The factor calculator does this automatically for any number.

Frequently asked questions about 441

What are the factors of 441?

The factors of 441 are 1, 3, 7, 9, 21, 49, 63, 147, and 441. That is 9 factors in total, counting both 1 and 441.

Is 441 a prime number?

No, 441 is not prime — it is a composite number with 9 factors. A prime number has exactly two factors, but 441 is also divisible by 3.

What is the prime factorization of 441?

The prime factorization of 441 is 3² × 7². Written out in full: 3 × 3 × 7 × 7 = 441. Its distinct prime factors are 3, 7.

What two numbers multiply to give 441?

There are 5 pairs of whole numbers that multiply to 441: 1 × 441, 3 × 147, 7 × 63, 9 × 49, 21 × 21.

What is the sum of the factors of 441?

Adding all the factors of 441 together gives 741. Excluding 441 itself, the proper factors sum to 300.

Is 441 a perfect square?

Yes, 441 is a perfect square. It equals 21 × 21. Perfect squares always have an odd number of factors — 441 has 9.

What is the largest factor of 441 other than itself?

The largest factor of 441 apart from 441 itself is 147, since 441 ÷ 147 = 3.

How many factors does 441 have?

441 has 9 factors: 1, 3, 7, 9, 21, 49, 63, 147, and 441. You can verify this from the prime factorization 3² × 7²: add 1 to each exponent and multiply, giving 3 × 3 = 9.

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.