Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 15, 20 i.e. 5 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 15 and 20 is **5**.

GCF(15,20) = 5

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

- Greatest Common Factor of 15 and 20 by prime factorization method
- Greatest Common Factor of 15 and 20 by matching factors method

**Prime Factorization of 15**

3 | 15 |

5 | 5 |

1 |

Prime factors of 15 are 3,5. Prime factorization of **15** in exponential form is:

15 = 3^{1}×5^{1}

**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}

∴ So by taking common prime factors GCF of 15 and 20 is 5

**Factors of 15**

List of positive integer factors of 15 that divides 15 without a remainder.

1,3,5,15

**Factors of 20**

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

1,2,4,5,10,20

**Greatest Common Factor**

We found the factors and prime factorization of 15 and 20. The biggest common factor number is the **GCF** number.

So the **greatest common factor 15 and 20** is **5**.

Also check out the Least Common Multiple of 15 and 20

(i) The GCF of 15 and 20 is associative

GCF of 15 and 20 = GCF of 20 and 15

1. What is the GCF of 15 and 20?

Answer: GCF of 15 and 20 is 5.

2. What are the Factors of 15?

Answer: Factors of 15 are 1, 3, 5, 15. There are 4 integers that are factors of 15. The greatest factor of 15 is 15.

3. 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.

4. How to Find the GCF of 15 and 20?

Answer:

Greatest Common Factor of 15 and 20 = 5

Step 1: Find the prime factorization of 15

15 = 3 x 5

Step 2: Find the prime factorization of 20

20 = 2 x 2 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 15 and 20 is 5