Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 721, 725 i.e. 1 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 721 and 725 is **1**.

GCF(721,725) = 1

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

- Greatest Common Factor of 721 and 725 by prime factorization method
- Greatest Common Factor of 721 and 725 by matching factors method

**Prime Factorization of 721**

7 | 721 |

103 | 103 |

1 |

Prime factors of 721 are 7,103. Prime factorization of **721** in exponential form is:

721 = 7^{1}×103^{1}

**Prime Factorization of 725**

5 | 725 |

5 | 145 |

29 | 29 |

1 |

Prime factors of 725 are 5,29. Prime factorization of **725** in exponential form is:

725 = 5^{2}×29^{1}

∴ So by taking common prime factors GCF of 721 and 725 is 1

**Factors of 721**

List of positive integer factors of 721 that divides 721 without a remainder.

1,7,103,721

**Factors of 725**

List of positive integer factors of 725 that divides 725 without a remainder.

1,5,25,29,145,725

**Greatest Common Factor**

We found the factors and prime factorization of 721 and 725. The biggest common factor number is the **GCF** number.

So the **greatest common factor 721 and 725** is **1**.

Also check out the Least Common Multiple of 721 and 725

(i) The GCF of 721 and 725 is associative

GCF of 721 and 725 = GCF of 725 and 721

1. What is the GCF of 721 and 725?

Answer: GCF of 721 and 725 is 1.

2. What are the Factors of 721?

Answer: Factors of 721 are 1, 7, 103, 721. There are 4 integers that are factors of 721. The greatest factor of 721 is 721.

3. What are the Factors of 725?

Answer: Factors of 725 are 1, 5, 25, 29, 145, 725. There are 6 integers that are factors of 725. The greatest factor of 725 is 725.

4. How to Find the GCF of 721 and 725?

Answer:

Greatest Common Factor of 721 and 725 = 1

Step 1: Find the prime factorization of 721

721 = 7 x 103

Step 2: Find the prime factorization of 725

725 = 5 x 5 x 29

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 721 and 725 is 1