Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 20, 25 i.e. 5 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 20 and 25 is **5**.

GCF(20,25) = 5

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

- Greatest Common Factor of 20 and 25 by prime factorization method
- Greatest Common Factor of 20 and 25 by matching factors method

**Prime Factorization of 20**

2 | 20 |

2 | 10 |

5 | 5 |

1 |

Prime factors of 20 are 2,5. Prime factorization of **20** in exponential form is:

20 = 2^{2}×5^{1}

**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}

∴ So by taking common prime factors GCF of 20 and 25 is 5

**Factors of 20**

List of positive integer factors of 20 that divides 20 without a remainder.

1,2,4,5,10,20

**Factors of 25**

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

1,5,25

**Greatest Common Factor**

We found the factors and prime factorization of 20 and 25. The biggest common factor number is the **GCF** number.

So the **greatest common factor 20 and 25** is **5**.

Also check out the Least Common Multiple of 20 and 25

(i) The GCF of 20 and 25 is associative

GCF of 20 and 25 = GCF of 25 and 20

1. What is the GCF of 20 and 25?

Answer: GCF of 20 and 25 is 5.

2. What are the Factors of 20?

Answer: Factors of 20 are 1, 2, 4, 5, 10, 20. There are 6 integers that are factors of 20. The greatest factor of 20 is 20.

3. 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.

4. How to Find the GCF of 20 and 25?

Answer:

Greatest Common Factor of 20 and 25 = 5

Step 1: Find the prime factorization of 20

20 = 2 x 2 x 5

Step 2: Find the prime factorization of 25

25 = 5 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 20 and 25 is 5