**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, 524 i.e. 1 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 517 and 524 is **1**.

GCF(517,524) = 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 524**

2 | 524 |

2 | 262 |

131 | 131 |

1 |

Prime factors of 524 are 2,131. Prime factorization of **524** in exponential form is:

524 = 2^{2}×131^{1}

∴ So by taking common prime factors GCF of 517 and 524 is 1

**Factors of 517**

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

1,11,47,517

**Factors of 524**

List of positive integer factors of 524 that divides 524 without a remainder.

1,2,4,131,262,524

**Greatest Common Factor**

We found the factors and prime factorization of 517 and 524. The biggest common factor number is the **GCF** number.

So the **greatest common factor 517 and 524** is **1**.

Also check out the Least Common Multiple of 517 and 524

(i) The GCF of 517 and 524 is associative

GCF of 517 and 524 = GCF of 524 and 517

1. What is the GCF of 517 and 524?

Answer: GCF of 517 and 524 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 524?

Answer: Factors of 524 are 1, 2, 4, 131, 262, 524. There are 6 integers that are factors of 524. The greatest factor of 524 is 524.

4. How to Find the GCF of 517 and 524?

Answer:

Greatest Common Factor of 517 and 524 = 1

Step 1: Find the prime factorization of 517

517 = 11 x 47

Step 2: Find the prime factorization of 524

524 = 2 x 2 x 131

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 524 is 1