Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 14, 21 i.e. 7 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 14 and 21 is **7**.

GCF(14,21) = 7

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

- Greatest Common Factor of 14 and 21 by prime factorization method
- Greatest Common Factor of 14 and 21 by matching factors method

**Prime Factorization of 14**

2 | 14 |

7 | 7 |

1 |

Prime factors of 14 are 2,7. Prime factorization of **14** in exponential form is:

14 = 2^{1}×7^{1}

**Prime Factorization of 21**

3 | 21 |

7 | 7 |

1 |

Prime factors of 21 are 3,7. Prime factorization of **21** in exponential form is:

21 = 3^{1}×7^{1}

∴ So by taking common prime factors GCF of 14 and 21 is 7

**Factors of 14**

List of positive integer factors of 14 that divides 14 without a remainder.

1,2,7,14

**Factors of 21**

List of positive integer factors of 21 that divides 21 without a remainder.

1,3,7,21

**Greatest Common Factor**

We found the factors and prime factorization of 14 and 21. The biggest common factor number is the **GCF** number.

So the **greatest common factor 14 and 21** is **7**.

Also check out the Least Common Multiple of 14 and 21

(i) The GCF of 14 and 21 is associative

GCF of 14 and 21 = GCF of 21 and 14

1. What is the GCF of 14 and 21?

Answer: GCF of 14 and 21 is 7.

2. What are the Factors of 14?

Answer: Factors of 14 are 1, 2, 7, 14. There are 4 integers that are factors of 14. The greatest factor of 14 is 14.

3. What are the Factors of 21?

Answer: Factors of 21 are 1, 3, 7, 21. There are 4 integers that are factors of 21. The greatest factor of 21 is 21.

4. How to Find the GCF of 14 and 21?

Answer:

Greatest Common Factor of 14 and 21 = 7

Step 1: Find the prime factorization of 14

14 = 2 x 7

Step 2: Find the prime factorization of 21

21 = 3 x 7

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

GCF = 7

Step 4: Therefore, the greatest common factor of 14 and 21 is 7