Factor Calculator

Factors of 410

The factors of 410 are 1, 2, 5, 10, 41, 82, 205, and 410. In total, 410 has 8 factors. Its prime factorization is 2 × 5 × 41, and the sum of all its factors is 756.

All factors of 410

Here are all 8 factors of 410, listed from smallest to largest.

125104182205410

Factor pairs of 410

These 4 pairs of whole numbers each multiply to give 410.

1 × 410 = 410
2 × 205 = 410
5 × 82 = 410
10 × 41 = 410

Prime factorization of 410

Dividing 410 by the smallest prime at each step gives its prime factorization:

410 ÷ 2 = 205
205 ÷ 5 = 41
41 ÷ 41 = 1
Result: 410 = 2 × 5 × 41 = 2 × 5 × 41

The distinct prime factors of 410 are 2, 5, 41. To factorize any other number, use the prime factorization calculator.

Factor tree of 410

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

Factor tree of 4104102205541
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 410

Number of factors8
Sum of factors756
Sum of proper factors346
Prime factorization2 × 5 × 41
Prime or composite?Composite
Even or odd?Even
Perfect square?No
Perfect cube?No
ClassificationDeficient

What makes 410 interesting

  • 410 is a composite number, meaning it has more than two factors. It can be written as a product of smaller whole numbers in 4 different ways.
  • 410 is a deficient number: its proper factors sum to 346, which is 64 less than 410 itself.
  • 410 has 3 distinct prime factors (2, 5, 41), which is why it has so many divisors.

How to find the factors of 410 yourself

Divide 410 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 √41020.25, because every factor above that pairs with one below it.

410 ÷ 1 = 410
410 ÷ 2 = 205
410 ÷ 5 = 82
410 ÷ 10 = 41

Reading both columns gives every factor: 1, 2, 5, 10, 41, 82, 205, 410. The factor calculator does this automatically for any number.

Frequently asked questions about 410

What are the factors of 410?

The factors of 410 are 1, 2, 5, 10, 41, 82, 205, and 410. That is 8 factors in total, counting both 1 and 410.

Is 410 a prime number?

No, 410 is not prime — it is a composite number with 8 factors. A prime number has exactly two factors, but 410 is also divisible by 2.

What is the prime factorization of 410?

The prime factorization of 410 is 2 × 5 × 41. Written out in full: 2 × 5 × 41 = 410. Its distinct prime factors are 2, 5, 41.

What two numbers multiply to give 410?

There are 4 pairs of whole numbers that multiply to 410: 1 × 410, 2 × 205, 5 × 82, 10 × 41.

What is the sum of the factors of 410?

Adding all the factors of 410 together gives 756. Excluding 410 itself, the proper factors sum to 346.

Is 410 a perfect square?

No, 410 is not a perfect square. There is no whole number that multiplies by itself to give 410. The nearest perfect squares are 400 and 441.

What is the largest factor of 410 other than itself?

The largest factor of 410 apart from 410 itself is 205, since 410 ÷ 205 = 2.

How many factors does 410 have?

410 has 8 factors: 1, 2, 5, 10, 41, 82, 205, and 410. You can verify this from the prime factorization 2 × 5 × 41: add 1 to each exponent and multiply, giving 2 × 2 × 2 = 8.

Explore more

Try another number in the factor calculator, break 410 down further with the prime factorization calculator, or compare 410 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.