Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 10, 12 i.e. 2 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 10 and 12 is **2**.

GCF(10,12) = 2

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

- Greatest Common Factor of 10 and 12 by prime factorization method
- Greatest Common Factor of 10 and 12 by matching factors method

**Prime Factorization of 10**

2 | 10 |

5 | 5 |

1 |

Prime factors of 10 are 2,5. Prime factorization of **10** in exponential form is:

10 = 2^{1}×5^{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 10 and 12 is 2

**Factors of 10**

List of positive integer factors of 10 that divides 10 without a remainder.

1,2,5,10

**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 10 and 12. The biggest common factor number is the **GCF** number.

So the **greatest common factor 10 and 12** is **2**.

Also check out the Least Common Multiple of 10 and 12

(i) The GCF of 10 and 12 is associative

GCF of 10 and 12 = GCF of 12 and 10

1. What is the GCF of 10 and 12?

Answer: GCF of 10 and 12 is 2.

2. What are the Factors of 10?

Answer: Factors of 10 are 1, 2, 5, 10. There are 4 integers that are factors of 10. The greatest factor of 10 is 10.

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 10 and 12?

Answer:

Greatest Common Factor of 10 and 12 = 2

Step 1: Find the prime factorization of 10

10 = 2 x 5

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

Step 4: Therefore, the greatest common factor of 10 and 12 is 2