# Factors of 54

The factors of 54 are the numbers that divide 54 evenly without leaving a remainder. These factors can be paired in a way that when multiplied together, they result in 54. These pairs are called factor pairs. Factors must be whole numbers and cannot be fractions.

## Introduction

Factors of 54 are the whole numbers that can be either positive or negative but cannot be decimal or fractional numbers. To find the factors of a number, you can use the prime factorization method.

## Factors of 54

1, 2, 3, 6, 9, 18, 27, 54

## Key properties of factors

- A factor of a number is its exact divisor.
- The number 1 is a factor of every number.
- A factor must always be less than or equal to the number.
- The greatest factor of any number is the number itself.

**Also Check: Cube root table**

## Prime Factorization Method

Prime factorization is a method used to determine the prime factors of 54. This involves breaking down 54 into its prime components. Here’s how you can do it:

- Start with the number 54.
- Divide 54 by the smallest prime number, which is 2.
- Continue dividing the result by the smallest prime number until you get a quotient of 1.

## Prime Factorization of 54

54÷2=27

27÷3=9

9÷3=3

3÷3=1

So, the prime factors of 54 are 2 and 3 (where 3 is repeated twice). This can be written as 2 x 3 x 3 x 3.

**Also Check: Differential Equations**

## Prime Factors of 54 by Division Method

To find the prime factors of 54 using the division method:

- Divide 54 by the smallest prime number (2).
- Continue dividing the quotient by the smallest prime number.
- Repeat this process until the quotient is 1.

**Example:**

54÷2=27

27÷3=9

9÷3=3

3÷3=1

So, the prime factors of 54 are 2 and 3 (3 appears three times).

## Pair Factors of 54

Pair factors are pairs of numbers that, when multiplied, give the original number, 54.

### Positive Pair Factors of 54:

1×54=54

2×27=54

3×18=54

6×9=54

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

**Also Check: Cubes from 1 to 50**

## Factor Tree of 54

A factor tree visually breaks down 54 into its prime factors.

From this factor tree, we can see that the prime factors of 54 are 2 and 3.

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## Frequently Asked Questions on Factors of 54

The prime factors of 54 are the prime numbers that divide 54 completely. Thus, the prime factors of 54 are 2 and 3.

No, the factors and multiples of 54 are different. Factors of 54 are numbers that divide 54 completely, while multiples of 54 are obtained by multiplying 54 by any integer.

The factors of 54 are numbers that divide 54 without leaving a remainder. The factors of 54 are 1, 2, 3, 6, 9, 18, 27, and 54.

The factor pairs of 54 are (1, 54), (2, 27), (3, 18), and (6, 9). The pair (6, 9) consists of both composite numbers.