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Factors of 520

Factors of 520 are integers that can be divided evenly into 520. There are total 16 factors of 520, of which 2, 5, 13 are its prime factors. The sum of all factors of 520 is 1260.

  • All Factors of 520: 1, 2, 4, 5, 8, 10, 13, 20, 26, 40, 52, 65, 104, 130, 260 and 520
  • Prime Factors of 520: 2, 5, 13
  • Prime Factorization of 520: 23 × 51 × 131
  • Sum of Factors of 520: 1260
1. What Are the Factors of 520?
2. Factors of 520 by Prime Factorization
3. Factors of 520 in Pairs
4. FAQs on Factors of 520
Factors of 520

What are Factors of 520?

Factors of 520 are pairs of those numbers whose products result in 520. These factors are either prime numbers or composite numbers.

How to Find the Factors of 520?

To find the factors of 520, we will have to find the list of numbers that would divide 520 without leaving any remainder.

  • 520/130 = 4; therefore, 130 is a factor of 520 and 4 is also a factor of 520.
  • 520/104 = 5; therefore, 104 is a factor of 520 and 5 is also a factor of 520.
Similarly we can find other factors. Hence, the factors of 520 are 1, 2, 4, 5, 8, 10, 13, 20, 26, 40, 52, 65, 104, 130, 260, 520.

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Factors of 520 by Prime Factorization

The number 520 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 520. The first step is to divide the number 520 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.
  • 520 ÷ 2 = 260
  • 260 ÷ 2 = 130
  • 130 ÷ 2 = 65

Further dividing 65 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 65 by the next smallest prime factor. We stop ultimately if the next prime factor doesn't exist or when we can't divide any further.

So, the prime factorization of 520 can be written as 23 × 51 × 131 where 2, 5, 13 are prime.

 

Factors of 520 in Pairs

Pair factors of 520 are the pairs of numbers that when multiplied give the product 520. The factors of 520 in pairs are:

  • 1 × 520 = (1, 520)
  • 2 × 260 = (2, 260)
  • 4 × 130 = (4, 130)
  • 5 × 104 = (5, 104)
  • 8 × 65 = (8, 65)
  • 10 × 52 = (10, 52)
  • 13 × 40 = (13, 40)
  • 20 × 26 = (20, 26)

Negative pair factors of 520 are:

  • -1 × -520 = (-1, -520)
  • -2 × -260 = (-2, -260)
  • -4 × -130 = (-4, -130)
  • -5 × -104 = (-5, -104)
  • -8 × -65 = (-8, -65)
  • -10 × -52 = (-10, -52)
  • -13 × -40 = (-13, -40)
  • -20 × -26 = (-20, -26)

NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.

Factors of 520 Solved Examples

  1. Example 1: How many factors are there for 520?

    Solution:

    The factors of 520 are too many, therefore if we can find the prime factorization of 520, then the total number of factors can be calculated using the formula shown below.
    If the prime factorization of the number is ax × by × cz where a, b, c are prime, then the total number of factors can be given by (x + 1)(y + 1)(z + 1).

    Prime Factorization of 520 = 23 × 51 × 131
    Therefore, the total number of factors are (3 + 1) × (1 + 1) × (1 + 1) = 4 × 2 × 2 = 16

  2. Example 2: Find the Least Common Multiple and Greatest Common Divisor (GCD) of 520 and 494.

    Solution:

    The factors of 520 are 1, 2, 4, 5, 8, 10, 13, 20, 26, 40, 52, 65, 104, 130, 260, 520 and factors of 494 are 1, 2, 13, 19, 26, 38, 247, 494.

    Therefore, the Least Common Multiple of 520 and 494 is 9880 and Greatest Common Divisor (GCD) of 520 and 494 is 26.

  3. Example 3: Find if 2, 5, 8, 20, 40, 122, 130 and 260 are factors of 520.

    Solution:

    When we divide 520 by 122 it leaves a remainder. Therefore, the number 122 is not a factor of 520. All numbers except 122 are factors of 520.

  4. Example 4: Find the product of all the prime factors of 520.

    Solution:

    Since, the prime factors of 520 are 2, 5, 13. Therefore, the product of prime factors = 2 × 5 × 13 = 130.

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FAQs on Factors of 520

What are the Factors of 520?

The factors of 520 are 1, 2, 4, 5, 8, 10, 13, 20, 26, 40, 52, 65, 104, 130, 260, 520 and its negative factors are -1, -2, -4, -5, -8, -10, -13, -20, -26, -40, -52, -65, -104, -130, -260, -520.

What is the Sum of all Factors of 520?

Sum of all factors of 520 = (23 + 1 - 1)/(2 - 1) × (51 + 1 - 1)/(5 - 1) × (131 + 1 - 1)/(13 - 1) = 1260

What are the Pair Factors of 520?

The pair factors of 520 are (1, 520), (2, 260), (4, 130), (5, 104), (8, 65), (10, 52), (13, 40), (20, 26).

What is the Greatest Common Factor of 520 and 104?

The factors of 520 and 104 are 1, 2, 4, 5, 8, 10, 13, 20, 26, 40, 52, 65, 104, 130, 260, 520 and 1, 2, 4, 8, 13, 26, 52, 104 respectively.

Common factors of 520 and 104 are [1, 2, 4, 8, 13, 26, 52, 104].

Hence, the Greatest Common Factor (GCF) of 520 and 104 is 104.

How Many Factors of 520 are also common to the Factors of 478?

Since, the factors of 520 are 1, 2, 4, 5, 8, 10, 13, 20, 26, 40, 52, 65, 104, 130, 260, 520 and the factors of 478 are 1, 2, 239, 478.
Hence, [1, 2] are the common factors of 520 and 478.

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