**Created By :**
Jatin Gogia

**Reviewed By :**
Rajasekhar Valipishetty

**Last Updated :**
Apr 06, 2023

Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 517, 519 i.e. 1 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 517 and 519 is **1**.

GCF(517,519) = 1

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

**Prime Factorization of 517**

11 | 517 |

47 | 47 |

1 |

Prime factors of 517 are 11,47. Prime factorization of **517** in exponential form is:

517 = 11^{1}×47^{1}

**Prime Factorization of 519**

3 | 519 |

173 | 173 |

1 |

Prime factors of 519 are 3,173. Prime factorization of **519** in exponential form is:

519 = 3^{1}×173^{1}

∴ So by taking common prime factors GCF of 517 and 519 is 1

**Factors of 517**

List of positive integer factors of 517 that divides 517 without a remainder.

1,11,47,517

**Factors of 519**

List of positive integer factors of 519 that divides 519 without a remainder.

1,3,173,519

**Greatest Common Factor**

We found the factors and prime factorization of 517 and 519. The biggest common factor number is the **GCF** number.

So the **greatest common factor 517 and 519** is **1**.

Also check out the Least Common Multiple of 517 and 519

(i) The GCF of 517 and 519 is associative

GCF of 517 and 519 = GCF of 519 and 517

1. What is the GCF of 517 and 519?

Answer: GCF of 517 and 519 is 1.

2. What are the Factors of 517?

Answer: Factors of 517 are 1, 11, 47, 517. There are 4 integers that are factors of 517. The greatest factor of 517 is 517.

3. What are the Factors of 519?

Answer: Factors of 519 are 1, 3, 173, 519. There are 4 integers that are factors of 519. The greatest factor of 519 is 519.

4. How to Find the GCF of 517 and 519?

Answer:

Greatest Common Factor of 517 and 519 = 1

Step 1: Find the prime factorization of 517

517 = 11 x 47

Step 2: Find the prime factorization of 519

519 = 3 x 173

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 517 and 519 is 1