Factor Calculator

Factors of 405

The factors of 405 are 1, 3, 5, 9, 15, 27, 45, 81, 135, and 405. In total, 405 has 10 factors. Its prime factorization is 3⁴ × 5, and the sum of all its factors is 726.

All factors of 405

Here are all 10 factors of 405, listed from smallest to largest.

135915274581135405

Factor pairs of 405

These 5 pairs of whole numbers each multiply to give 405.

1 × 405 = 405
3 × 135 = 405
5 × 81 = 405
9 × 45 = 405
15 × 27 = 405

Prime factorization of 405

Dividing 405 by the smallest prime at each step gives its prime factorization:

405 ÷ 3 = 135
135 ÷ 3 = 45
45 ÷ 3 = 15
15 ÷ 3 = 5
5 ÷ 5 = 1
Result: 405 = 3 × 3 × 3 × 3 × 5 = 3⁴ × 5

The distinct prime factors of 405 are 3, 5. To factorize any other number, use the prime factorization calculator.

Factor tree of 405

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

Factor tree of 405405313534531535
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 405

Number of factors10
Sum of factors726
Sum of proper factors321
Prime factorization3⁴ × 5
Prime or composite?Composite
Even or odd?Odd
Perfect square?No
Perfect cube?No
ClassificationDeficient

What makes 405 interesting

  • 405 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.
  • 405 is a deficient number: its proper factors sum to 321, which is 84 less than 405 itself.

How to find the factors of 405 yourself

Divide 405 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 √405 ≈ 20.12, because every factor above that pairs with one below it.

405 ÷ 1 = 405 ✓
405 ÷ 3 = 135 ✓
405 ÷ 5 = 81 ✓
405 ÷ 9 = 45 ✓
405 ÷ 15 = 27 ✓

Reading both columns gives every factor: 1, 3, 5, 9, 15, 27, 45, 81, 135, 405. The factor calculator does this automatically for any number.

Numbers mathematically connected to 405.

Frequently asked questions about 405

What are the factors of 405?

The factors of 405 are 1, 3, 5, 9, 15, 27, 45, 81, 135, and 405. That is 10 factors in total, counting both 1 and 405.

Is 405 a prime number?

No, 405 is not prime — it is a composite number with 10 factors. A prime number has exactly two factors, but 405 is also divisible by 3.

What is the prime factorization of 405?

The prime factorization of 405 is 3⁴ × 5. Written out in full: 3 × 3 × 3 × 3 × 5 = 405. Its distinct prime factors are 3, 5.

What two numbers multiply to give 405?

There are 5 pairs of whole numbers that multiply to 405: 1 × 405, 3 × 135, 5 × 81, 9 × 45, 15 × 27.

What is the sum of the factors of 405?

Adding all the factors of 405 together gives 726. Excluding 405 itself, the proper factors sum to 321.

Is 405 a perfect square?

No, 405 is not a perfect square. There is no whole number that multiplies by itself to give 405. The nearest perfect squares are 400 and 441.

What is the largest factor of 405 other than itself?

The largest factor of 405 apart from 405 itself is 135, since 405 ÷ 135 = 3.

How many factors does 405 have?

405 has 10 factors: 1, 3, 5, 9, 15, 27, 45, 81, 135, and 405. You can verify this from the prime factorization 3⁴ × 5: add 1 to each exponent and multiply, giving 5 × 2 = 10.

Explore more

Try another number in the factor calculator, break 405 down further with the prime factorization calculator, or compare 405 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.