Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 720, 725 i.e. 5 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 720 and 725 is **5**.

GCF(720,725) = 5

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

- Greatest Common Factor of 720 and 725 by prime factorization method
- Greatest Common Factor of 720 and 725 by matching factors method

**Prime Factorization of 720**

2 | 720 |

2 | 360 |

2 | 180 |

2 | 90 |

3 | 45 |

3 | 15 |

5 | 5 |

1 |

Prime factors of 720 are 2,3,5. Prime factorization of **720** in exponential form is:

720 = 2^{4}×3^{2}×5^{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 720 and 725 is 5

**Factors of 720**

List of positive integer factors of 720 that divides 720 without a remainder.

1,2,3,4,5,6,8,9,10,12,15,16,18,20,24,30,36,40,45,48,60,72,80,90,120,144,180,240,360,720

**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 720 and 725. The biggest common factor number is the **GCF** number.

So the **greatest common factor 720 and 725** is **5**.

Also check out the Least Common Multiple of 720 and 725

(i) The GCF of 720 and 725 is associative

GCF of 720 and 725 = GCF of 725 and 720

1. What is the GCF of 720 and 725?

Answer: GCF of 720 and 725 is 5.

2. What are the Factors of 720?

Answer: Factors of 720 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 120, 144, 180, 240, 360, 720. There are 30 integers that are factors of 720. The greatest factor of 720 is 720.

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 720 and 725?

Answer:

Greatest Common Factor of 720 and 725 = 5

Step 1: Find the prime factorization of 720

720 = 2 x 2 x 2 x 2 x 3 x 3 x 5

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 = 5

Step 4: Therefore, the greatest common factor of 720 and 725 is 5