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Factors of 54

Factors of 54 are the list of integers that can be evenly divided into 54. There are overall 8 factors of 54 among which 54 is the biggest factor and its positive factors are 1, 2, 3, 6, 9, 18, 27 and 54. The Pair Factors of 54 are (1, 54), (2, 27), (3, 18), and (6, 9) and its Prime Factors are 1, 2, 3, 6, 9, 18, 27, 54.

  • Factors of 54: 1, 2, 3, 6, 9, 18, 27 and 54
  • Negative Factors of 54: -1, -2, -3, -6, -9, -18, -27 and -54
  • Prime Factors of 54: 2, 3
  • Prime Factorization of 54: 2 × 3 × 3 × 3 = 2 × 33
  • Sum of Factors of 54: 120

 

1. What Are the Factors of 54?
2. How to Calculate Factors of 54?
3. Factors of 54 by Prime Factorization
4. Factors of 54 in Pairs
5. FAQs on Factors of 54

What are the Factors of 54?

Before we move ahead, let’s recall a little about factors. A factor is a number that divides the given number without any remainder. The factors of 54 are pairs of those numbers whose products results in 54

factors of 54

How to Calculate the Factors of 54?

To calculate the factors of any number, here in this case 54, we need to find all the numbers that would divide 54 without leaving any remainder. We start with the number 1, then check for numbers 2, 3, 4, 5, 6, 7, etc up to 54 respectively. The number 1 and the number itself would always be a factor of the given number.

We express 54 as a product of its prime factors in the prime factorization method as well as we divide 54 with its divisors in the division method. Let us see which numbers divide 54 exactly without a  remainder. The divisors, as well as the quotients, are the factors of 54

  • 54 ÷ 1 = 54, therefore, 1 and 24 is a factor of 54
  • 54 ÷ 2 = 27, therefore, 2 is a factor of 54
  • 54 ÷ 3 = 18, therefore, 3 is a factor of 54
  • 54 ÷ 6 = 9, therefore, 6 is a factor of 54

Hence, the factors of 54 are 1, 2, 3, 6, 9, 18, 27 and 54

To understand the concept of finding factors by prime factorization better, let us take a few more examples.

Important Notes

  • While finding factors of any number, we consider only whole numbers and integers.
  • Decimal numbers and fractions are not considered as factors of a number.
  • All even numbers will definitely have 2 as its factor.

Factors of 54 by Prime Factorization

Factors of 54 by prime factorization are given by using the following steps. In the first step write the pair of factors, which on multiplication gives the required number. 54 can be factored as a product of 6 and 9.  In the second step See the factors, whether each one of them is prime or not. 6 is not a prime number and can be dissociated as a product of 2 by 3. 9 is not a prime number and can be dissociated as a product of 3 by the square of 3 in step three, as per the criteria, 54 can be written as 54 = 6 × 9 = 2 × 3 × 3 × 3. It can also be written as 54 = 2 × 33.
Observe below the prime factorization of 54

prime factorization of 54

Factors of 54 in Pairs

Pair factors are pairs of those numbers which when multiplied, give the product as the required number.

Factors of 54 in pairs can be written as:

Factors Pair factors
1 × 54 = 54 1, 54 
2 × 27 = 54 2, 27
3 × 18 = 54  3, 18 
6 × 9  = 54  6, 9
9 × 6 = 54  9, 6 
18 × 3 = 54  18, 3 
27 × 2 = 54  27, 2 
54 × 1 = 54 54, 1 

The above given factors are positive pair factors. 

It is possible to have negative pair factors as well because the product of two negative numbers also gives a positive number.

Let's have a look at negative pair factors. 

Factors Pair factors
-1 × -54 = 54 (-1, -54) 
-2 × -27 = 54 (-2, -27)
-3 × -18 = 54 ( -3, -18) 
-6 × -9  = 54  (-6, -9)
-9 × -6 = 54 ( -9, -6) 
-18 × -3 = 54  (18, -3 )   
-27 × -2 = 54 ( -27, -2 ) 
-54 × -1 = 54  (-54, -1 )
 

Factors of 54 Solved Examples

  1. Example 1: James, Judy, and Christina pluck 54 oranges and distribute them among themselves equally. How many oranges will each of them get? 

    Solution:

    54 oranges are to be divided among James, Judy, and Christina equally.
    So for this, we need to divide the number 54 by 3
    54 ÷ 3=18
    Hence each child will get 18 oranges.

  2. Example 2: Help Ruth in finding the following factors of 54.

    a. Half of 54?
    b. Two-third of 54?

    Solution

    a. 54 ÷ 2=27
    b. 54 × 2 ÷ 3 = 36
    But 36 is not a factor of 54
    So, no factor of 54 is two-third of 54

  3. Example 3: Give one-factor pair of 54 which contains both composite numbers.

    Solution

    The possible factor pairs of 54 are (1, 54), (2, 27), (3, 18), (6, 9)
    1, 2, and 3 are not composite.
    So, out of all these pairs, only (6, 9) has both the factors as composite numbers.

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FAQs on Factors of 54

What are the Factors of 54?

The factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54 and its negative factors are -1, -2, -3, -6, -9, -18, -27, -54.

What is the Greatest Common Factor of 54 and 49?

The factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54 and the factors of 49 are 1, 7, 49. 54 and 49 have only one common factor which is 1. This implies that 54 and 49 are co-prime.

Hence, the Greatest Common Factor (GCF) of 54 and 49 is 1.

What is the Sum of the Factors of 54?

Sum of all factors of 54 = (21 + 1 - 1)/(2 - 1) × (33 + 1 - 1)/(3 - 1) = 120

What Numbers Are the Prime Factors of 54?

The prime factors of 54 are 2, 3.

How Many Factors of 34 are also Common to the Factors of 54?

Since, the factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54 and the factors of 34 are 1, 2, 17, 34.
Hence, [1, 2] are the common factors of 54 and 34.

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