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Factors of 546

Factors of 546 are the list of integers that we can split evenly into 546. There are overall 16 factors of 546 among which 546 is the biggest factor and 2, 3, 7, 13 are its prime factors. The sum of all factors of 546 is 1344.

  • All Factors of 546: 1, 2, 3, 6, 7, 13, 14, 21, 26, 39, 42, 78, 91, 182, 273 and 546
  • Prime Factors of 546: 2, 3, 7, 13
  • Prime Factorization of 546: 21 × 31 × 71 × 131
  • Sum of Factors of 546: 1344
1. What Are the Factors of 546?
2. Factors of 546 by Prime Factorization
3. Factors of 546 in Pairs
4. FAQs on Factors of 546
Factors of 546

What are Factors of 546?

Factors of 546 are pairs of those numbers whose products result in 546. These factors are either prime numbers or composite numbers.

How to Find the Factors of 546?

To find the factors of 546, we will have to find the list of numbers that would divide 546 without leaving any remainder.

  • 546/273 = 2; therefore, 273 is a factor of 546 and 2 is also a factor of 546.
  • 546/42 = 13; therefore, 42 is a factor of 546 and 13 is also a factor of 546.
Similarly we can find other factors. Hence, the factors of 546 are 1, 2, 3, 6, 7, 13, 14, 21, 26, 39, 42, 78, 91, 182, 273, 546.

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Factors of 546 by Prime Factorization

The number 546 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 546. The first step is to divide the number 546 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.
  • 546 ÷ 2 = 273

Further dividing 273 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 273 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 546 can be written as 21 × 31 × 71 × 131 where 2, 3, 7, 13 are prime.

 

Factors of 546 in Pairs

Pair factors of 546 are the pairs of numbers that when multiplied give the product 546. The factors of 546 in pairs are:

  • 1 × 546 = (1, 546)
  • 2 × 273 = (2, 273)
  • 3 × 182 = (3, 182)
  • 6 × 91 = (6, 91)
  • 7 × 78 = (7, 78)
  • 13 × 42 = (13, 42)
  • 14 × 39 = (14, 39)
  • 21 × 26 = (21, 26)

Negative pair factors of 546 are:

  • -1 × -546 = (-1, -546)
  • -2 × -273 = (-2, -273)
  • -3 × -182 = (-3, -182)
  • -6 × -91 = (-6, -91)
  • -7 × -78 = (-7, -78)
  • -13 × -42 = (-13, -42)
  • -14 × -39 = (-14, -39)
  • -21 × -26 = (-21, -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 546 Solved Examples

  1. Example 1: How many factors are there for 546?

    Solution:

    The factors of 546 are too many, therefore if we can find the prime factorization of 546, 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 546 = 21 × 31 × 71 × 131
    Therefore, the total number of factors are (1 + 1) × (1 + 1) × (1 + 1) × (1 + 1) = 2 × 2 × 2 × 2 = 16

  2. Example 2: Find the Lowest Common Multiple (LCM) and Greatest Common Divisor (GCD) of 546 and 443.

    Solution:

    The factors of 546 are 1, 2, 3, 6, 7, 13, 14, 21, 26, 39, 42, 78, 91, 182, 273, 546 and factors of 443 are 1, 443.

    Therefore, the Lowest Common Multiple (LCM) of 546 and 443 is 241878 and Greatest Common Divisor (GCD) of 546 and 443 is 1.

  3. Example 3: Find if 1, 6, 7, 39, 78, 182, 273 and 477 are factors of 546.

    Solution:

    When we divide 546 by 477 it leaves a remainder. Therefore, the number 477 is not a factor of 546. All numbers except 477 are factors of 546.

  4. Example 4: Find the product of all the prime factors of 546.

    Solution:

    Since, the prime factors of 546 are 2, 3, 7, 13. Therefore, the product of prime factors = 2 × 3 × 7 × 13 = 546.

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FAQs on Factors of 546

What are the Factors of 546?

The factors of 546 are 1, 2, 3, 6, 7, 13, 14, 21, 26, 39, 42, 78, 91, 182, 273, 546 and its negative factors are -1, -2, -3, -6, -7, -13, -14, -21, -26, -39, -42, -78, -91, -182, -273, -546.

What is the Sum of Factors of 546?

Sum of all factors of 546 = (21 + 1 - 1)/(2 - 1) × (31 + 1 - 1)/(3 - 1) × (71 + 1 - 1)/(7 - 1) × (131 + 1 - 1)/(13 - 1) = 1344

What are Prime Factors of 546?

The prime factors of 546 are 2, 3, 7, 13.

What is the Greatest Common Factor of 546 and 459?

The factors of 546 and 459 are 1, 2, 3, 6, 7, 13, 14, 21, 26, 39, 42, 78, 91, 182, 273, 546 and 1, 3, 9, 17, 27, 51, 153, 459 respectively.

Common factors of 546 and 459 are [1, 3].

Hence, the Greatest Common Factor of 546 and 459 is 3.

How Many Factors of 546 are also Factors of 256?

Since, the factors of 546 are 1, 2, 3, 6, 7, 13, 14, 21, 26, 39, 42, 78, 91, 182, 273, 546 and the factors of 256 are 1, 2, 4, 8, 16, 32, 64, 128, 256.
Hence, [1, 2] are the common factors of 546 and 256.

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