Factors of 54

The factors of 54 are the numbers, that produce the result as 54 when two numbers are multiplied together. Consider an example, the factor pairs of 41 is written as (1,41) and (-1,-41). When we multiply the pair of negative factors, the result should give the original number, such as multiplying -1  × -41, then we get the number 41. Thus, we can consider both positive and negative factor pairs of 41. Factor pairs of the number 54 are the whole numbers which could be either positive or negative but not a fraction or decimal number. To find the factors of a number, 54, we will use the factorization method.

Factors of 54

In the factorization method, first consider the numbers, 1 and 54 as factors and continue with finding the other pair of multiples of 54 which gives the results as an original number. To understand this method in a better way, read the article below to find the factors in pairs. Also, the prime factors of a number 54 with the help of the division method are discussed here. Some important properties of factors are:

  • A factor of any given number is its exact divisor
  • For every number, 1 is a factor.
  • The factor should be always less than or equal to the number itself
  • The number itself is considered as the greatest factor of a number.

Factors

Factors of 54
1, 2, 3, 6, 9, 18, 27, and 54

Prime Factors of 54 By Division Method

The number 54 is a composite and it should have prime factors. Now let us know how to calculate the prime factors of 54.

  • The first step is to divide the number 54 with the smallest prime factor, say 2.

           54 ÷ 2 = 27

  • Again, when you divide 54 by 3, you will get a fractional number and it cannot be a   factor and continue with the next prime factor, say 3

           27 ÷ 3 = 9

           9 ÷ 3 = 3

           3 ÷ 3 = 1

  • Finally, we received the number 1 at the end of the division process. So that we cannot proceed further. So, the prime factors of 54 are written as 2 × 3 × 3 × 3 or 2x 33, where 2 and 3 are the prime numbers.

Pair Factors of 54

To find the pair factors, multiply the two numbers in a pair to get the original number as 54, such numbers are as follows

1 × 54 = 54, (1, 54) is a pair factor of 54.

2 × 27 = 54, (2, 27) is a pair factor of 54

3 × 18 = 54, (3, 18) is a pair factor of 54

6 × 9 = 54, (6, 9) is a pair factor of 54

Therefore, the positive pair factors are (1, 54), (2, 27),(3, 18) and (6, 9).

To find the negative pair factors of 54, then proceed with the following steps

-1 × -54 = 54, (-1, -54) is a pair factor of 54.

-2 × -27 = 54, (-2, -27) is a pair factor of 54

-3 × -18 = 54, (-3, -18) is a pair factor of 54

-6 × -9 = 54, (-6, -9) is a pair factor of 54

Therefore, the negative pair factors are (-1, -54), (-2, -27),(-3, -18) and (-6,- 9).

How to calculate the Factors of 54?

Learn the following steps to calculate the factors of a number 54

  • First, write the number 54
  • Find the two numbers, which gives the result as 54 under the multiplication, say 2 and 27, such as 2 × 27 = 54.
  • We know that 2 is a prime number which has only two factors, i.e., 1 and the number itself( 1 and 2). So, it cannot be further factorized.

2 = 2 × 1

  • But look at the number 27, which is a composite number but not a prime number. So it can be further factorized.

27 =  3 × 3 × 3 × 1

  • Therefore, the factorization of 54 is written as 54 = 2 x 3 × 3 × 3 × 1

Stay tuned with BYJU’S to know about factors of 54 and also learn the prime factors of other numbers. To clarify the doubts, watch interactive videos for better understanding.

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