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Factors of 540

Factors of 540 are numbers that, when multiplied in pairs give the product as 540. There are 24 factors of 540, of which the following are its prime factors 2, 3, 5. The Prime Factorization of 540 is 22 × 33 × 51.

  • All Factors of 540: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270 and 540
  • Prime Factors of 540: 2, 3, 5
  • Prime Factorization of 540: 22 × 33 × 51
  • Sum of Factors of 540: 1680
1. What Are the Factors of 540?
2. Factors of 540 by Prime Factorization
3. Factors of 540 in Pairs
4. FAQs on Factors of 540
Factors of 540

What are Factors of 540?

Factors of 540 are pairs of those numbers whose products result in 540. These factors are either prime numbers or composite numbers.

How to Find the Factors of 540?

To find the factors of 540, we will have to find the list of numbers that would divide 540 without leaving any remainder.

  • 540/36 = 15; therefore, 36 is a factor of 540 and 15 is also a factor of 540.
  • 540/2 = 270; therefore, 2 is a factor of 540 and 270 is also a factor of 540.
Similarly we can find other factors. Hence, the factors of 540 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270, 540.

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Factors of 540 by Prime Factorization

The number 540 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 540. The first step is to divide the number 540 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.
  • 540 ÷ 2 = 270
  • 270 ÷ 2 = 135

Further dividing 135 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 135 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 540 can be written as 22 × 33 × 51 where 2, 3, 5 are prime.

 

Factors of 540 in Pairs

Pair factors of 540 are the pairs of numbers that when multiplied give the product 540. The factors of 540 in pairs are:

  • 1 × 540 = (1, 540)
  • 2 × 270 = (2, 270)
  • 3 × 180 = (3, 180)
  • 4 × 135 = (4, 135)
  • 5 × 108 = (5, 108)
  • 6 × 90 = (6, 90)
  • 9 × 60 = (9, 60)
  • 10 × 54 = (10, 54)
  • 12 × 45 = (12, 45)
  • 15 × 36 = (15, 36)
  • 18 × 30 = (18, 30)
  • 20 × 27 = (20, 27)

Negative pair factors of 540 are:

  • -1 × -540 = (-1, -540)
  • -2 × -270 = (-2, -270)
  • -3 × -180 = (-3, -180)
  • -4 × -135 = (-4, -135)
  • -5 × -108 = (-5, -108)
  • -6 × -90 = (-6, -90)
  • -9 × -60 = (-9, -60)
  • -10 × -54 = (-10, -54)
  • -12 × -45 = (-12, -45)
  • -15 × -36 = (-15, -36)
  • -18 × -30 = (-18, -30)
  • -20 × -27 = (-20, -27)

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

Factors of 540 Solved Examples

  1. Example 1: How many factors are there for 540?

    Solution:

    The factors of 540 are too many, therefore if we can find the prime factorization of 540, 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 540 = 22 × 33 × 51
    Therefore, the total number of factors are (2 + 1) × (3 + 1) × (1 + 1) = 3 × 4 × 2 = 24

  2. Example 2: Find the Least Common Multiple (LCM) and Greatest Common Factor (GCF) of 540 and 270.

    Solution:

    The factors of 540 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270, 540 and factors of 270 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, 270.

    Therefore, the Least Common Multiple (LCM) of 540 and 270 is 540 and Greatest Common Factor (GCF) of 540 and 270 is 270.

  3. Example 3: Find if 1, 9, 12, 15, 30, 37, 54 and 180 are factors of 540.

    Solution:

    When we divide 540 by 37 it leaves a remainder. Therefore, the number 37 is not a factor of 540. All numbers except 37 are factors of 540.

  4. Example 4: Find the product of all the prime factors of 540.

    Solution:

    Since, the prime factors of 540 are 2, 3, 5. Therefore, the product of prime factors = 2 × 3 × 5 = 30.

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FAQs on Factors of 540

What are the Factors of 540?

The factors of 540 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270, 540 and its negative factors are -1, -2, -3, -4, -5, -6, -9, -10, -12, -15, -18, -20, -27, -30, -36, -45, -54, -60, -90, -108, -135, -180, -270, -540.

What is the Sum of all Factors of 540?

Sum of all factors of 540 = (22 + 1 - 1)/(2 - 1) × (33 + 1 - 1)/(3 - 1) × (51 + 1 - 1)/(5 - 1) = 1680

What are Pair Factors of 540?

The pair factors of 540 are (1, 540), (2, 270), (3, 180), (4, 135), (5, 108), (6, 90), (9, 60), (10, 54), (12, 45), (15, 36), (18, 30), (20, 27).

What is the Greatest Common Factor of 540 and 128?

The factors of 540 and 128 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270, 540 and 1, 2, 4, 8, 16, 32, 64, 128 respectively.

Common factors of 540 and 128 are [1, 2, 4].

Hence, the Greatest Common Factor of 540 and 128 is 4.

How Many Factors of 540 are also Factors of 33?

Since, the factors of 540 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270, 540 and the factors of 33 are 1, 3, 11, 33.
Hence, [1, 3] are the common factors of 540 and 33.

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