# Factors of 54

Understanding the factors of a number is essential in both mathematics and everyday life. In this comprehensive guide, we will explore the factors of 54, breaking down how to find them, pair them, and conduct prime factorization. We will also discuss negative pair factors and factor trees for a holistic understanding of the topic.

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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
Factors of 54 in Pairs: (1, 54), (2, 27), (3, 18) and (6, 9)

## How to Find Factors of 54

Here’s a step-by-step guide on finding the factors of 54:

(i) 54 ÷ 1 = 54

This division gives the remainder 0 and so is divisible by 54. So please put them 1 and 54 in your factor list.

1, … 54

(ii) 54 ÷ 2 = 27

This division gives the remainder 0 and so is divisible by 27. So please put them 2 and 27 in your factor list.

1, 2 … 27, 54

(iii) 54 ÷ 3 = 18

This division gives the remainder 0 and so is divisible by 18. So please put them 3 and 18 in your factor list.

1, 2, 3 … 18, 27, 54

(iv) 54 ÷ 4 = 13.5

This division gives the remainder 13.5, not being thoroughly divided. So we will not write 4 and 13.5 on the list.

(v) 54 ÷ 5 = 10.8

This division gives the remainder 10.8, not being thoroughly divided. So we will not write 5 and 10.8 on the list.

(vi) 54 ÷ 6 = 9

This division gives the remainder 0 and so is divisible by 9. So please put them 6 and 9 in your factor list.

1, 2, 3, 6 … 9, 18, 27, 54

(vi) Since we don’t have any more numbers to calculate, we are putting the numbers so far.

So 1, 2, 3, 6, 9, 18, 27 and 54 are factors of 54.

### Factor Pairs of 54

Factor pairs are sets of two numbers that, when multiplied together, give the original number. The factor pairs of 54 are:

1 x 54 = 54
2 x 27 = 54
3 x 18 = 54
6 x 9 = 54

So, (1, 54), (2, 27), (3, 18) and (6, 9) are factor pairs of 54

### Negative Pair Factors of 54

Negative factors are simply the negative counterparts of positive factors. To find the negative pair factors of 54, just add a minus sign to the positive factors:

-1 x -54 = 54
-2 x -27 = 54
-3 x -18 = 54
-6 x -9 = 54

So, (-1, -54), (-2, -27), (-3, -18) and (-6, -9) are factor pairs of 54

### Prime Factorization of 54

Prime factorization is the process of breaking down a number into its smallest prime factors. Here’s how to find the prime factorization of 54:

54 ÷ 2 = 27
27 ÷ 3 = 9
9 ÷ 3 = 3
3 ÷ 3 = 1

### Factor Tree of 54

A factor tree is a visual representation of the prime factorization process. Here’s a factor tree for 54:

``````   54
/  \
2    27
/  \
3    9
/  \
3    3
``````