**Definition of factors of 54:** If a number completely divides 54 without leaving a remainder, then that number is called a factor of 54.

Thus, we can say that the factors of 54 are the divisors of 54. In this section, we will learn about the factors of 54 and the prime factors of 54. Note that we have:

**54=2×3×3×3=2×3**is the prime factorization of 54.^{3}- The factors of 54 are 1, 2, 3, 6, 9, 18, 27, and 54.
- The prime factors of 54 are 2 and 3.
- Negative factors of 54 are –1, -2, -3,-6, -9, -18, -27, and –54.

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## What are the Factors of 54?

Let us write the number 54 multiplicatively in all possible ways. We definitely have:

54 = 1×54

54 = 2×27

54 = 3×18

54 = 6×9

As there are no numbers between 6 and 9 that can divide 54, so we will stop writing 54 multiplicatively right now. So the factors of 54 in pairs are given as follows:

54 = a×b | Factors in Pairs (a,b) |

54 = 1×54 | (1, 54) |

54 = 2×27 | (2, 27) |

54 = 3×18 | (3, 18) |

54 = 6×9 | (6, 9) |

Thus the pair factors of 54 are (1, 54), (2, 27), (3, 18), and (6, 9). As all the numbers appearing in pair factors are the factors of 54, we conclude that

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

## Number of Factors of 54

From above we have calculated the factors of 54 which are 1, 2, 3, 6, 9, 18, 27, and 54.

Thus the total number of factors of 54 is eight.

## Prime Factors of 54

Note that the factors of 54 are 1, 2, 3, 6, 9, 18, 27, and 54. Among those factors, we observe that only 2 and 3 are prime numbers as they do not have any proper divisors.

∴ the prime factors of 54 are 2 and 3.

Question: What are the factors of 54?

Video Solution:

## How to Find Factors of 54?

Now we will determine the factors of 54 by **division method**. In this method, we will try to find the numbers that can divide 54 with no remainder. See that

54/1=54 and the remainder is 0.

∴ 1 and 54 are factors of 54.

54/2=27 and the remainder is 0.

∴ 2 and 27 are factors of 54.

54/3=18 and the remainder is 0.

∴ 3 and 18 are factors of 54.

54/6=9 and the remainder is 0.

∴ 6 and 9 are factors of 54.

Note that no numbers other than the numbers in violet color can divide 54. So the numbers in violet color, that is, 1, 2, 3, 6, 9, 18, 27, and 54 are the complete list of factors of 54.

**Also Read: **

- Basic concepts of factors
- Square root of 54
- Cube root of 54
- Divisors of 54