Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 6, 15 i.e. 3 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 6 and 15 is **3**.

GCF(6,15) = 3

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

- Greatest Common Factor of 6 and 15 by prime factorization method
- Greatest Common Factor of 6 and 15 by matching factors method

**Prime Factorization of 6**

2 | 6 |

3 | 3 |

1 |

Prime factors of 6 are 2,3. Prime factorization of **6** in exponential form is:

6 = 2^{1}×3^{1}

**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}

∴ So by taking common prime factors GCF of 6 and 15 is 3

**Factors of 6**

List of positive integer factors of 6 that divides 6 without a remainder.

1,2,3,6

**Factors of 15**

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

1,3,5,15

**Greatest Common Factor**

We found the factors and prime factorization of 6 and 15. The biggest common factor number is the **GCF** number.

So the **greatest common factor 6 and 15** is **3**.

Also check out the Least Common Multiple of 6 and 15

(i) The GCF of 6 and 15 is associative

GCF of 6 and 15 = GCF of 15 and 6

1. What is the GCF of 6 and 15?

Answer: GCF of 6 and 15 is 3.

2. What are the Factors of 6?

Answer: Factors of 6 are 1, 2, 3, 6. There are 4 integers that are factors of 6. The greatest factor of 6 is 6.

3. 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.

4. How to Find the GCF of 6 and 15?

Answer:

Greatest Common Factor of 6 and 15 = 3

Step 1: Find the prime factorization of 6

6 = 2 x 3

Step 2: Find the prime factorization of 15

15 = 3 x 5

Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:

GCF = 3

Step 4: Therefore, the greatest common factor of 6 and 15 is 3