The different Factors of 54 are the numbers which when divided 54 completely leaving remainder 0 and multiplied in pairs give the product as 54. These factors can be positive as well as negative. The number 54 is also an even composite number, which means that it has several factors. In this lesson, we will calculate the factors of 54, prime factors of 54, and factors of 54 in pairs along with solved examples for a better understanding.

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

**Prime Factorization of 54: **54 = 2 × 3^{3}

**Table of Contents**

- What Are the Factors of 54?
- How to Calculate Factors of 54?
- Important Notes
- Factors of 54 by Prime Factorization
- Factors of 54 in Pairs
- FAQs on Factors of 54
- Tips And Tricks
- Solved Examples
- Interactive Questions

## 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

## 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.

- Factors of 51 - The factors of 51 are 1, 3, 17, 51.
- Factors of 52 - The factors of 52 are 1, 2, 13, 52.
- Factors of 55 - The factors of 55 are 1, 5, 11, 55.
- Factors of 56 - The factors of 56 are 1, 2, 4, 7, 8, 14, 56
- Factors of 48 - The factors of 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

**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 number 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 × 3^{3}.

Observe below the 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 |

**These 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 ) |

## FAQs on Factors of 54

### 1. What are the common factors of 54 and 56?

The common factors of 54 and 56 are 1 and 2.

### 2. What are the factors of 54 and 36?

The factors of 54 are : 1, 2, 3, 6, 9, 18, 27, 54

The factors of 36 are : 1, 2, 3, 4, 6, 9, 12, 18, 36

### 3. Is 54 composite or prime?

54 is a composite number as it has more than two factors.

### 4. How many factors of 54 are perfect squares?

Among all the factors of 54, 9 is a perfect square 9^{ }= 3^{²}.

### 5. What is the highest common factors of 18 and 54?

The highest common factor of 54 and 18 is 18.

**Tips and Tricks**

- 1 is the smallest factor of every number.
- Every number has a minimum of two factors, i.e. 1 and the number itself.

## Factors of 54 Solved Examples

**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.

**Example:2** Help Ruth in finding the followig 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

**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.

## Interactive Questions

**Here are a few activities for you to practice. **

**Select/Type your answer and click the "Check Answer" button to see the result.**