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Factors of 528

Factors of 528 are the list of integers that we can split evenly into 528. There are total 20 factors of 528, of which 2, 3, 11 are its prime factors. The sum of all factors of 528 is 1488.

  • All Factors of 528: 1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 33, 44, 48, 66, 88, 132, 176, 264 and 528
  • Prime Factors of 528: 2, 3, 11
  • Prime Factorization of 528: 24 × 31 × 111
  • Sum of Factors of 528: 1488
1. What Are the Factors of 528?
2. Factors of 528 by Prime Factorization
3. Factors of 528 in Pairs
4. FAQs on Factors of 528
Factors of 528

What are Factors of 528?

Factors of 528 are pairs of those numbers whose products result in 528. These factors are either prime numbers or composite numbers.

How to Find the Factors of 528?

To find the factors of 528, we will have to find the list of numbers that would divide 528 without leaving any remainder.

  • 528/132 = 4; therefore, 132 is a factor of 528 and 4 is also a factor of 528.
  • 528/66 = 8; therefore, 66 is a factor of 528 and 8 is also a factor of 528.
Similarly we can find other factors. Hence, the factors of 528 are 1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 33, 44, 48, 66, 88, 132, 176, 264, 528.

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Factors of 528 by Prime Factorization

The number 528 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 528. The first step is to divide the number 528 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.
  • 528 ÷ 2 = 264
  • 264 ÷ 2 = 132
  • 132 ÷ 2 = 66
  • 66 ÷ 2 = 33

Further dividing 33 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 33 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 528 can be written as 24 × 31 × 111 where 2, 3, 11 are prime.

 

Factors of 528 in Pairs

Pair factors of 528 are the pairs of numbers that when multiplied give the product 528. The factors of 528 in pairs are:

  • 1 × 528 = (1, 528)
  • 2 × 264 = (2, 264)
  • 3 × 176 = (3, 176)
  • 4 × 132 = (4, 132)
  • 6 × 88 = (6, 88)
  • 8 × 66 = (8, 66)
  • 11 × 48 = (11, 48)
  • 12 × 44 = (12, 44)
  • 16 × 33 = (16, 33)
  • 22 × 24 = (22, 24)

Negative pair factors of 528 are:

  • -1 × -528 = (-1, -528)
  • -2 × -264 = (-2, -264)
  • -3 × -176 = (-3, -176)
  • -4 × -132 = (-4, -132)
  • -6 × -88 = (-6, -88)
  • -8 × -66 = (-8, -66)
  • -11 × -48 = (-11, -48)
  • -12 × -44 = (-12, -44)
  • -16 × -33 = (-16, -33)
  • -22 × -24 = (-22, -24)

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

Factors of 528 Solved Examples

  1. Example 1: How many factors are there for 528?

    Solution:

    The factors of 528 are too many, therefore if we can find the prime factorization of 528, 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 528 = 24 × 31 × 111
    Therefore, the total number of factors are (4 + 1) × (1 + 1) × (1 + 1) = 5 × 2 × 2 = 20

  2. Example 2: Find the LCM and Greatest Common Divisor (GCD) of 528 and 24.

    Solution:

    The factors of 528 are 1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 33, 44, 48, 66, 88, 132, 176, 264, 528 and factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24.

    Therefore, the LCM of 528 and 24 is 528 and Greatest Common Divisor (GCD) of 528 and 24 is 24.

  3. Example 3: Find if 6, 8, 11, 12, 66, 176, 455 and 528 are factors of 528.

    Solution:

    When we divide 528 by 455 it leaves a remainder. Therefore, the number 455 is not a factor of 528. All numbers except 455 are factors of 528.

  4. Example 4: Find the product of all the prime factors of 528.

    Solution:

    Since, the prime factors of 528 are 2, 3, 11. Therefore, the product of prime factors = 2 × 3 × 11 = 66.

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FAQs on Factors of 528

What are the Factors of 528?

The factors of 528 are 1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 33, 44, 48, 66, 88, 132, 176, 264, 528 and its negative factors are -1, -2, -3, -4, -6, -8, -11, -12, -16, -22, -24, -33, -44, -48, -66, -88, -132, -176, -264, -528.

What is the Sum of all Factors of 528?

Sum of all factors of 528 = (24 + 1 - 1)/(2 - 1) × (31 + 1 - 1)/(3 - 1) × (111 + 1 - 1)/(11 - 1) = 1488

What are the Pair Factors of 528?

The pair factors of 528 are (1, 528), (2, 264), (3, 176), (4, 132), (6, 88), (8, 66), (11, 48), (12, 44), (16, 33), (22, 24).

What is the Greatest Common Factor of 528 and 356?

The factors of 528 and 356 are 1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 33, 44, 48, 66, 88, 132, 176, 264, 528 and 1, 2, 4, 89, 178, 356 respectively.

Common factors of 528 and 356 are [1, 2, 4].

Hence, the GCF of 528 and 356 is 4.

How Many Factors of 528 are also Factors of 172?

Since, the factors of 528 are 1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 33, 44, 48, 66, 88, 132, 176, 264, 528 and the factors of 172 are 1, 2, 4, 43, 86, 172.
Hence, [1, 2, 4] are the common factors of 528 and 172.

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