Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 108, 111 i.e. 3 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 108 and 111 is **3**.

GCF(108,111) = 3

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

- Greatest Common Factor of 108 and 111 by prime factorization method
- Greatest Common Factor of 108 and 111 by matching factors method

**Prime Factorization of 108**

2 | 108 |

2 | 54 |

3 | 27 |

3 | 9 |

3 | 3 |

1 |

Prime factors of 108 are 2,3. Prime factorization of **108** in exponential form is:

108 = 2^{2}×3^{3}

**Prime Factorization of 111**

3 | 111 |

37 | 37 |

1 |

Prime factors of 111 are 3,37. Prime factorization of **111** in exponential form is:

111 = 3^{1}×37^{1}

∴ So by taking common prime factors GCF of 108 and 111 is 3

**Factors of 108**

List of positive integer factors of 108 that divides 108 without a remainder.

1,2,3,4,6,9,12,18,27,36,54,108

**Factors of 111**

List of positive integer factors of 111 that divides 111 without a remainder.

1,3,37,111

**Greatest Common Factor**

We found the factors and prime factorization of 108 and 111. The biggest common factor number is the **GCF** number.

So the **greatest common factor 108 and 111** is **3**.

Also check out the Least Common Multiple of 108 and 111

(i) The GCF of 108 and 111 is associative

GCF of 108 and 111 = GCF of 111 and 108

1. What is the GCF of 108 and 111?

Answer: GCF of 108 and 111 is 3.

2. What are the Factors of 108?

Answer: Factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108. There are 12 integers that are factors of 108. The greatest factor of 108 is 108.

3. What are the Factors of 111?

Answer: Factors of 111 are 1, 3, 37, 111. There are 4 integers that are factors of 111. The greatest factor of 111 is 111.

4. How to Find the GCF of 108 and 111?

Answer:

Greatest Common Factor of 108 and 111 = 3

Step 1: Find the prime factorization of 108

108 = 2 x 2 x 3 x 3 x 3

Step 2: Find the prime factorization of 111

111 = 3 x 37

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

GCF = 3

Step 4: Therefore, the greatest common factor of 108 and 111 is 3