Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 14, 19 i.e. 1 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 14 and 19 is **1**.

GCF(14,19) = 1

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

- Greatest Common Factor of 14 and 19 by prime factorization method
- Greatest Common Factor of 14 and 19 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 19**

19 | 19 |

1 |

Prime factors of 19 are 19. Prime factorization of **19** in exponential form is:

19 = 19^{1}

∴ So by taking common prime factors GCF of 14 and 19 is 1

**Factors of 14**

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

1,2,7,14

**Factors of 19**

List of positive integer factors of 19 that divides 19 without a remainder.

1,19

**Greatest Common Factor**

We found the factors and prime factorization of 14 and 19. The biggest common factor number is the **GCF** number.

So the **greatest common factor 14 and 19** is **1**.

Also check out the Least Common Multiple of 14 and 19

(i) The GCF of 14 and 19 is associative

GCF of 14 and 19 = GCF of 19 and 14

1. What is the GCF of 14 and 19?

Answer: GCF of 14 and 19 is 1.

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 19?

Answer: Factors of 19 are 1, 19. There are 2 integers that are factors of 19. The greatest factor of 19 is 19.

4. How to Find the GCF of 14 and 19?

Answer:

Greatest Common Factor of 14 and 19 = 1

Step 1: Find the prime factorization of 14

14 = 2 x 7

Step 2: Find the prime factorization of 19

19 = 19

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

GCF = = 1

Step 4: Therefore, the greatest common factor of 14 and 19 is 1