Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 6, 12 i.e. 6 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 6 and 12 is **6**.

GCF(6,12) = 6

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

- Greatest Common Factor of 6 and 12 by prime factorization method
- Greatest Common Factor of 6 and 12 by matching factors method

**Prime Factorization of 6**

2 | 6 |

3 | 3 |

1 |

Prime factors of 6 are 2,3. Prime factorization of **6** in exponential form is:

6 = 2^{1}×3^{1}

**Prime Factorization of 12**

2 | 12 |

2 | 6 |

3 | 3 |

1 |

Prime factors of 12 are 2,3. Prime factorization of **12** in exponential form is:

12 = 2^{2}×3^{1}

∴ So by taking common prime factors GCF of 6 and 12 is 6

**Factors of 6**

List of positive integer factors of 6 that divides 6 without a remainder.

1,2,3,6

**Factors of 12**

List of positive integer factors of 12 that divides 12 without a remainder.

1,2,3,4,6,12

**Greatest Common Factor**

We found the factors and prime factorization of 6 and 12. The biggest common factor number is the **GCF** number.

So the **greatest common factor 6 and 12** is **6**.

Also check out the Least Common Multiple of 6 and 12

(i) The GCF of 6 and 12 is associative

GCF of 6 and 12 = GCF of 12 and 6

1. What is the GCF of 6 and 12?

Answer: GCF of 6 and 12 is 6.

2. What are the Factors of 6?

Answer: Factors of 6 are 1, 2, 3, 6. There are 4 integers that are factors of 6. The greatest factor of 6 is 6.

3. What are the Factors of 12?

Answer: Factors of 12 are 1, 2, 3, 4, 6, 12. There are 6 integers that are factors of 12. The greatest factor of 12 is 12.

4. How to Find the GCF of 6 and 12?

Answer:

Greatest Common Factor of 6 and 12 = 6

Step 1: Find the prime factorization of 6

6 = 2 x 3

Step 2: Find the prime factorization of 12

12 = 2 x 2 x 3

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 6 and 12 is 6