**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 25, 30 i.e. 5 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 25 and 30 is **5**.

GCF(25,30) = 5

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

**Prime Factorization of 25**

5 | 25 |

5 | 5 |

1 |

Prime factors of 25 are 5. Prime factorization of **25** in exponential form is:

25 = 5^{2}

**Prime Factorization of 30**

2 | 30 |

3 | 15 |

5 | 5 |

1 |

Prime factors of 30 are 2.Prime factorization of **30** in exponential form is:

30 = 2^{1}×3^{1}×5^{1}

∴ So by taking common prime factors GCF of 25 and 30 is 5

**Factors of 25**

List of positive integer factors of 25 that divides 25 without a remainder.

1,5,25

**Factors of 30**

List of positive integer factors of 30 that divides 30 without a remainder.

1,2,3,5,6,10,15,30

**Greatest Common Factor**

We found the factors and prime factorization of 25 and 30. The biggest common factor number is the **GCF** number.

So the **greatest common factor 25 and 30** is **5**.

Also check out the Least Common Multiple of 25 and 30

(i) The GCF of 25 and 30 is associative

GCF of 25 and 30 = GCF of 30 and 25

1. What is the GCF of 25 and 30?

Answer: GCF of 25 and 30 is 5.

2. What are the Factors of 25?

Answer: Factors of 25 are 1, 5, 25. There are 3 integers that are factors of 25. The greatest factor of 25 is 25.

3. What are the Factors of 30?

Answer: Factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30. There are 8 integers that are factors of 30. The greatest factor of 30 is 30.

4. How to Find the GCF of 25 and 30?

Answer:

Greatest Common Factor of 25 and 30 = 5

Step 1: Find the prime factorization of 25

25 = 5 x 5

Step 2: Find the prime factorization of 30

30 = 2 x 3 x 5

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 25 and 30 is 5