Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 36, 42 i.e. 6 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 36 and 42 is **6**.

GCF(36,42) = 6

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

- Greatest Common Factor of 36 and 42 by prime factorization method
- Greatest Common Factor of 36 and 42 by matching factors method

**Prime Factorization of 36**

2 | 36 |

2 | 18 |

3 | 9 |

3 | 3 |

1 |

Prime factors of 36 are 2,3. Prime factorization of **36** in exponential form is:

36 = 2^{2}×3^{2}

**Prime Factorization of 42**

2 | 42 |

3 | 21 |

7 | 7 |

1 |

Prime factors of 42 are 2,3,7. Prime factorization of **42** in exponential form is:

42 = 2^{1}×3^{1}×7^{1}

∴ So by taking common prime factors GCF of 36 and 42 is 6

**Factors of 36**

List of positive integer factors of 36 that divides 36 without a remainder.

1,2,3,4,6,9,12,18,36

**Factors of 42**

List of positive integer factors of 42 that divides 42 without a remainder.

1,2,3,6,7,14,21,42

**Greatest Common Factor**

We found the factors and prime factorization of 36 and 42. The biggest common factor number is the **GCF** number.

So the **greatest common factor 36 and 42** is **6**.

Also check out the Least Common Multiple of 36 and 42

(i) The GCF of 36 and 42 is associative

GCF of 36 and 42 = GCF of 42 and 36

1. What is the GCF of 36 and 42?

Answer: GCF of 36 and 42 is 6.

2. What are the Factors of 36?

Answer: Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. There are 9 integers that are factors of 36. The greatest factor of 36 is 36.

3. What are the Factors of 42?

Answer: Factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42. There are 8 integers that are factors of 42. The greatest factor of 42 is 42.

4. How to Find the GCF of 36 and 42?

Answer:

Greatest Common Factor of 36 and 42 = 6

Step 1: Find the prime factorization of 36

36 = 2 x 2 x 3 x 3

Step 2: Find the prime factorization of 42

42 = 2 x 3 x 7

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

GCF = 2 x 3 = 6

Step 4: Therefore, the greatest common factor of 36 and 42 is 6