Factor Calculator

Factors of 510

The factors of 510 are 1, 2, 3, 5, 6, 10, 15, 17, 30, 34, 51, 85, 102, 170, 255, and 510. In total, 510 has 16 factors. Its prime factorization is 2 × 3 × 5 × 17, and the sum of all its factors is 1296.

All factors of 510

Here are all 16 factors of 510, listed from smallest to largest.

1235610151730345185102170255510

Factor pairs of 510

These 8 pairs of whole numbers each multiply to give 510.

1 × 510 = 510
2 × 255 = 510
3 × 170 = 510
5 × 102 = 510
6 × 85 = 510
10 × 51 = 510
15 × 34 = 510
17 × 30 = 510

Prime factorization of 510

Dividing 510 by the smallest prime at each step gives its prime factorization:

510 ÷ 2 = 255
255 ÷ 3 = 85
85 ÷ 5 = 17
17 ÷ 17 = 1
Result: 510 = 2 × 3 × 5 × 17 = 2 × 3 × 5 × 17

The distinct prime factors of 510 are 2, 3, 5, 17. To factorize any other number, use the prime factorization calculator.

Factor tree of 510

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

Factor tree of 5105102255385517
Prime factors are shown in solid indigo. Composite numbers split into their smallest prime and the quotient.

Properties of 510

Number of factors16
Sum of factors1296
Sum of proper factors786
Prime factorization2 × 3 × 5 × 17
Prime or composite?Composite
Even or odd?Even
Perfect square?No
Perfect cube?No
ClassificationAbundant

What makes 510 interesting

  • 510 is a composite number, meaning it has more than two factors. It can be written as a product of smaller whole numbers in 8 different ways.
  • 510 is an abundant number: its proper factors sum to 786, which is 276 more than 510 itself.
  • 510 has 4 distinct prime factors (2, 3, 5, 17), which is why it has so many divisors.

How to find the factors of 510 yourself

Divide 510 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 √510 ≈ 22.58, because every factor above that pairs with one below it.

510 ÷ 1 = 510 ✓
510 ÷ 2 = 255 ✓
510 ÷ 3 = 170 ✓
510 ÷ 5 = 102 ✓
510 ÷ 6 = 85 ✓
510 ÷ 10 = 51 ✓
510 ÷ 15 = 34 ✓
510 ÷ 17 = 30 ✓

Reading both columns gives every factor: 1, 2, 3, 5, 6, 10, 15, 17, 30, 34, 51, 85, 102, 170, 255, 510. The factor calculator does this automatically for any number.

Numbers mathematically connected to 510.

Frequently asked questions about 510

What are the factors of 510?

The factors of 510 are 1, 2, 3, 5, 6, 10, 15, 17, 30, 34, 51, 85, 102, 170, 255, and 510. That is 16 factors in total, counting both 1 and 510.

Is 510 a prime number?

No, 510 is not prime — it is a composite number with 16 factors. A prime number has exactly two factors, but 510 is also divisible by 2.

What is the prime factorization of 510?

The prime factorization of 510 is 2 × 3 × 5 × 17. Written out in full: 2 × 3 × 5 × 17 = 510. Its distinct prime factors are 2, 3, 5, 17.

What two numbers multiply to give 510?

There are 8 pairs of whole numbers that multiply to 510: 1 × 510, 2 × 255, 3 × 170, 5 × 102, 6 × 85, 10 × 51, 15 × 34, 17 × 30.

What is the sum of the factors of 510?

Adding all the factors of 510 together gives 1296. Excluding 510 itself, the proper factors sum to 786.

Is 510 a perfect square?

No, 510 is not a perfect square. There is no whole number that multiplies by itself to give 510. The nearest perfect squares are 484 and 529.

What is the largest factor of 510 other than itself?

The largest factor of 510 apart from 510 itself is 255, since 510 ÷ 255 = 2.

How many factors does 510 have?

510 has 16 factors: 1, 2, 3, 5, 6, 10, 15, 17, 30, 34, 51, 85, 102, 170, 255, and 510. You can verify this from the prime factorization 2 × 3 × 5 × 17: add 1 to each exponent and multiply, giving 2 × 2 × 2 × 2 = 16.

Explore more

Try another number in the factor calculator, break 510 down further with the prime factorization calculator, or compare 510 with another number using the GCF calculator and LCM calculator. For divisor counts and sums, see the divisor calculator.