Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 108, 110 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 108 and 110 is **2**.

GCF(108,110) = 2

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

- Greatest Common Factor of 108 and 110 by prime factorization method
- Greatest Common Factor of 108 and 110 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 110**

2 | 110 |

5 | 55 |

11 | 11 |

1 |

Prime factors of 110 are 2,5,11. Prime factorization of **110** in exponential form is:

110 = 2^{1}×5^{1}×11^{1}

∴ So by taking common prime factors GCF of 108 and 110 is 2

**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 110**

List of positive integer factors of 110 that divides 110 without a remainder.

1,2,5,10,11,22,55,110

**Greatest Common Factor**

We found the factors and prime factorization of 108 and 110. The biggest common factor number is the **GCF** number.

So the **greatest common factor 108 and 110** is **2**.

Also check out the Least Common Multiple of 108 and 110

(i) The GCF of 108 and 110 is associative

GCF of 108 and 110 = GCF of 110 and 108

1. What is the GCF of 108 and 110?

Answer: GCF of 108 and 110 is 2.

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 110?

Answer: Factors of 110 are 1, 2, 5, 10, 11, 22, 55, 110. There are 8 integers that are factors of 110. The greatest factor of 110 is 110.

4. How to Find the GCF of 108 and 110?

Answer:

Greatest Common Factor of 108 and 110 = 2

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 110

110 = 2 x 5 x 11

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

GCF = 2

Step 4: Therefore, the greatest common factor of 108 and 110 is 2