Factor Calculator

Factors of 407

The factors of 407 are 1, 11, 37, and 407. In total, 407 has 4 factors. Its prime factorization is 11 × 37, and the sum of all its factors is 456.

All factors of 407

Here are all 4 factors of 407, listed from smallest to largest.

11137407

Factor pairs of 407

These 2 pairs of whole numbers each multiply to give 407.

1 × 407 = 407
11 × 37 = 407

Prime factorization of 407

Dividing 407 by the smallest prime at each step gives its prime factorization:

407 ÷ 11 = 37
37 ÷ 37 = 1
Result: 407 = 11 × 37 = 11 × 37

The distinct prime factors of 407 are 11, 37. To factorize any other number, use the prime factorization calculator.

Factor tree of 407

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

Factor tree of 4074071137
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 407

Number of factors4
Sum of factors456
Sum of proper factors49
Prime factorization11 × 37
Prime or composite?Composite
Even or odd?Odd
Perfect square?No
Perfect cube?No
ClassificationDeficient

What makes 407 interesting

  • 407 is a composite number, meaning it has more than two factors. It can be written as a product of smaller whole numbers in 2 different ways.
  • 407 is a deficient number: its proper factors sum to 49, which is 358 less than 407 itself.

How to find the factors of 407 yourself

Divide 407 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 √40720.17, because every factor above that pairs with one below it.

407 ÷ 1 = 407
407 ÷ 11 = 37

Reading both columns gives every factor: 1, 11, 37, 407. The factor calculator does this automatically for any number.

Frequently asked questions about 407

What are the factors of 407?

The factors of 407 are 1, 11, 37, and 407. That is 4 factors in total, counting both 1 and 407.

Is 407 a prime number?

No, 407 is not prime — it is a composite number with 4 factors. A prime number has exactly two factors, but 407 is also divisible by 11.

What is the prime factorization of 407?

The prime factorization of 407 is 11 × 37. Written out in full: 11 × 37 = 407. Its distinct prime factors are 11, 37.

What two numbers multiply to give 407?

There are 2 pairs of whole numbers that multiply to 407: 1 × 407, 11 × 37.

What is the sum of the factors of 407?

Adding all the factors of 407 together gives 456. Excluding 407 itself, the proper factors sum to 49.

Is 407 a perfect square?

No, 407 is not a perfect square. There is no whole number that multiplies by itself to give 407. The nearest perfect squares are 400 and 441.

What is the largest factor of 407 other than itself?

The largest factor of 407 apart from 407 itself is 37, since 407 ÷ 37 = 11.

How many factors does 407 have?

407 has 4 factors: 1, 11, 37, and 407. You can verify this from the prime factorization 11 × 37: add 1 to each exponent and multiply, giving 2 × 2 = 4.

Explore more

Try another number in the factor calculator, break 407 down further with the prime factorization calculator, or compare 407 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.