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Factors of 564

Factors of 564 are the list of integers that we can split evenly into 564. There are 12 factors of 564, of which the following are its prime factors 2, 3, 47. The sum of all factors of 564 is 1344.

  • All Factors of 564: 1, 2, 3, 4, 6, 12, 47, 94, 141, 188, 282 and 564
  • Prime Factors of 564: 2, 3, 47
  • Prime Factorization of 564: 22 × 31 × 471
  • Sum of Factors of 564: 1344
1. What Are the Factors of 564?
2. Factors of 564 by Prime Factorization
3. Factors of 564 in Pairs
4. FAQs on Factors of 564
Factors of 564

What are Factors of 564?

Factors of 564 are pairs of those numbers whose products result in 564. These factors are either prime numbers or composite numbers.

How to Find the Factors of 564?

To find the factors of 564, we will have to find the list of numbers that would divide 564 without leaving any remainder.

  • 564/188 = 3; therefore, 188 is a factor of 564 and 3 is also a factor of 564.
  • 564/141 = 4; therefore, 141 is a factor of 564 and 4 is also a factor of 564.
Similarly we can find other factors. Hence, the factors of 564 are 1, 2, 3, 4, 6, 12, 47, 94, 141, 188, 282, 564.

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Factors of 564 by Prime Factorization

The number 564 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 564. The first step is to divide the number 564 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.
  • 564 ÷ 2 = 282
  • 282 ÷ 2 = 141

Further dividing 141 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 141 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 564 can be written as 22 × 31 × 471 where 2, 3, 47 are prime.

 

Factors of 564 in Pairs

Pair factors of 564 are the pairs of numbers that when multiplied give the product 564. The factors of 564 in pairs are:

  • 1 × 564 = (1, 564)
  • 2 × 282 = (2, 282)
  • 3 × 188 = (3, 188)
  • 4 × 141 = (4, 141)
  • 6 × 94 = (6, 94)
  • 12 × 47 = (12, 47)

Negative pair factors of 564 are:

  • -1 × -564 = (-1, -564)
  • -2 × -282 = (-2, -282)
  • -3 × -188 = (-3, -188)
  • -4 × -141 = (-4, -141)
  • -6 × -94 = (-6, -94)
  • -12 × -47 = (-12, -47)

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

Factors of 564 Solved Examples

  1. Example 1: How many factors are there for 564?

    Solution:

    The factors of 564 are too many, therefore if we can find the prime factorization of 564, 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 564 = 22 × 31 × 471
    Therefore, the total number of factors are (2 + 1) × (1 + 1) × (1 + 1) = 3 × 2 × 2 = 12

  2. Example 2: Find the LCM and Greatest Common Divisor (GCD) of 564 and 266.

    Solution:

    The factors of 564 are 1, 2, 3, 4, 6, 12, 47, 94, 141, 188, 282, 564 and factors of 266 are 1, 2, 7, 14, 19, 38, 133, 266.

    Therefore, the LCM of 564 and 266 is 75012 and Greatest Common Divisor (GCD) of 564 and 266 is 2.

  3. Example 3: Find if 1, 2, 4, 12, 116, 188 and 564 are factors of 564.

    Solution:

    When we divide 564 by 116 it leaves a remainder. Therefore, the number 116 is not a factor of 564. All numbers except 116 are factors of 564.

  4. Example 4: Find the product of all the prime factors of 564.

    Solution:

    Since, the prime factors of 564 are 2, 3, 47. Therefore, the product of prime factors = 2 × 3 × 47 = 282.

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FAQs on Factors of 564

What are the Factors of 564?

The factors of 564 are 1, 2, 3, 4, 6, 12, 47, 94, 141, 188, 282, 564 and its negative factors are -1, -2, -3, -4, -6, -12, -47, -94, -141, -188, -282, -564.

What is the Sum of all the Factors of 564?

Sum of all factors of 564 = (22 + 1 - 1)/(2 - 1) × (31 + 1 - 1)/(3 - 1) × (471 + 1 - 1)/(47 - 1) = 1344

What numbers are the Pair Factors of 564?

The pair factors of 564 are (1, 564), (2, 282), (3, 188), (4, 141), (6, 94), (12, 47).

What is the Greatest Common Factor of 564 and 101?

The factors of 564 are 1, 2, 3, 4, 6, 12, 47, 94, 141, 188, 282, 564 and the factors of 101 are 1, 101. 564 and 101 have only one common factor which is 1. This implies that 564 and 101 are co-prime.

Hence, the Greatest Common Factor (GCF) of 564 and 101 is 1.

What are the Common Factors of 564 and 25?

Since, the factors of 564 are 1, 2, 3, 4, 6, 12, 47, 94, 141, 188, 282, 564 and factors of 25 are 1, 5, 25. Hence, 564 and 25 have only one common factor which is 1. Therefore, 564 and 25 are co-prime.

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