Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 54, 60 i.e. 6 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 54 and 60 is **6**.

GCF(54,60) = 6

*Greatest common factor* or Greatest common divisor (GCD) can be calculated in following way;

- Greatest Common Factor of 54 and 60 by prime factorization method
- Greatest Common Factor of 54 and 60 by matching factors method

**Prime Factorization of 54**

2 | 54 |

3 | 27 |

3 | 9 |

3 | 3 |

1 |

Prime factors of 54 are 2,3. Prime factorization of **54** in exponential form is:

54 = 2^{1}×3^{3}

**Prime Factorization of 60**

2 | 60 |

2 | 30 |

3 | 15 |

5 | 5 |

1 |

Prime factors of 60 are 2,3,5. Prime factorization of **60** in exponential form is:

60 = 2^{2}×3^{1}×5^{1}

∴ So by taking common prime factors GCF of 54 and 60 is 6

**Factors of 54**

List of positive integer factors of 54 that divides 54 without a remainder.

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

**Factors of 60**

List of positive integer factors of 60 that divides 60 without a remainder.

1,2,3,4,5,6,10,12,15,20,30,60

**Greatest Common Factor**

We found the factors and prime factorization of 54 and 60. The biggest common factor number is the **GCF** number.

So the **greatest common factor 54 and 60** is **6**.

Also check out the Least Common Multiple of 54 and 60

(i) The GCF of 54 and 60 is associative

GCF of 54 and 60 = GCF of 60 and 54

1. What is the GCF of 54 and 60?

Answer: GCF of 54 and 60 is 6.

2. What are the Factors of 54?

Answer: Factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54. There are 8 integers that are factors of 54. The greatest factor of 54 is 54.

3. What are the Factors of 60?

Answer: Factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60. There are 12 integers that are factors of 60. The greatest factor of 60 is 60.

4. How to Find the GCF of 54 and 60?

Answer:

Greatest Common Factor of 54 and 60 = 6

Step 1: Find the prime factorization of 54

54 = 2 x 3 x 3 x 3

Step 2: Find the prime factorization of 60

60 = 2 x 2 x 3 x 5

Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:

GCF = 2 x 3 = 6

Step 4: Therefore, the greatest common factor of 54 and 60 is 6