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Factors of 522

Factors of 522 are the list of integers that can be evenly divided into 522. There are total 12 factors of 522, of which 2, 3, 29 are its prime factors. The sum of all factors of 522 is 1170.

  • All Factors of 522: 1, 2, 3, 6, 9, 18, 29, 58, 87, 174, 261 and 522
  • Prime Factors of 522: 2, 3, 29
  • Prime Factorization of 522: 21 × 32 × 291
  • Sum of Factors of 522: 1170
1. What Are the Factors of 522?
2. Factors of 522 by Prime Factorization
3. Factors of 522 in Pairs
4. FAQs on Factors of 522
Factors of 522

What are Factors of 522?

Factors of 522 are pairs of those numbers whose products result in 522. These factors are either prime numbers or composite numbers.

How to Find the Factors of 522?

To find the factors of 522, we will have to find the list of numbers that would divide 522 without leaving any remainder.

  • 522/9 = 58; therefore, 9 is a factor of 522 and 58 is also a factor of 522.
  • 522/87 = 6; therefore, 87 is a factor of 522 and 6 is also a factor of 522.
Similarly we can find other factors. Hence, the factors of 522 are 1, 2, 3, 6, 9, 18, 29, 58, 87, 174, 261, 522.

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Factors of 522 by Prime Factorization

The number 522 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 522. The first step is to divide the number 522 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.
  • 522 ÷ 2 = 261

Further dividing 261 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 261 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 522 can be written as 21 × 32 × 291 where 2, 3, 29 are prime.

 

Factors of 522 in Pairs

Pair factors of 522 are the pairs of numbers that when multiplied give the product 522. The factors of 522 in pairs are:

  • 1 × 522 = (1, 522)
  • 2 × 261 = (2, 261)
  • 3 × 174 = (3, 174)
  • 6 × 87 = (6, 87)
  • 9 × 58 = (9, 58)
  • 18 × 29 = (18, 29)

Negative pair factors of 522 are:

  • -1 × -522 = (-1, -522)
  • -2 × -261 = (-2, -261)
  • -3 × -174 = (-3, -174)
  • -6 × -87 = (-6, -87)
  • -9 × -58 = (-9, -58)
  • -18 × -29 = (-18, -29)

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

Factors of 522 Solved Examples

  1. Example 1: How many factors are there for 522?

    Solution:

    The factors of 522 are too many, therefore if we can find the prime factorization of 522, 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 522 = 21 × 32 × 291
    Therefore, the total number of factors are (1 + 1) × (2 + 1) × (1 + 1) = 2 × 3 × 2 = 12

  2. Example 2: Find the LCM and Greatest Common Factor (GCF) of 522 and 495.

    Solution:

    The factors of 522 are 1, 2, 3, 6, 9, 18, 29, 58, 87, 174, 261, 522 and factors of 495 are 1, 3, 5, 9, 11, 15, 33, 45, 55, 99, 165, 495.

    Therefore, the LCM of 522 and 495 is 28710 and Greatest Common Factor (GCF) of 522 and 495 is 9.

  3. Example 3: Find if 1, 3, 58, 87, 174, 196 and 522 are factors of 522.

    Solution:

    When we divide 522 by 196 it leaves a remainder. Therefore, the number 196 is not a factor of 522. All numbers except 196 are factors of 522.

  4. Example 4: Find the product of all the prime factors of 522.

    Solution:

    Since, the prime factors of 522 are 2, 3, 29. Therefore, the product of prime factors = 2 × 3 × 29 = 174.

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FAQs on Factors of 522

What are the Factors of 522?

The factors of 522 are 1, 2, 3, 6, 9, 18, 29, 58, 87, 174, 261, 522 and its negative factors are -1, -2, -3, -6, -9, -18, -29, -58, -87, -174, -261, -522.

What is the Sum of all Factors of 522?

Sum of all factors of 522 = (21 + 1 - 1)/(2 - 1) × (32 + 1 - 1)/(3 - 1) × (291 + 1 - 1)/(29 - 1) = 1170

What are the Prime Factors of 522?

The prime factors of 522 are 2, 3, 29.

What is the Greatest Common Factor of 522 and 57?

The factors of 522 and 57 are 1, 2, 3, 6, 9, 18, 29, 58, 87, 174, 261, 522 and 1, 3, 19, 57 respectively.

Common factors of 522 and 57 are [1, 3].

Hence, the Greatest Common Factor (GCF) of 522 and 57 is 3.

How Many Factors of 522 are also common to the Factors of 125?

Since, the factors of 522 are 1, 2, 3, 6, 9, 18, 29, 58, 87, 174, 261, 522 and factors of 125 are 1, 5, 25, 125. Hence, 522 and 125 have only one common factor which is 1. Therefore, 522 and 125 are co-prime.

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