Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 36, 72 i.e. 36 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 36 and 72 is **36**.

GCF(36,72) = 36

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

- Greatest Common Factor of 36 and 72 by prime factorization method
- Greatest Common Factor of 36 and 72 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 72**

2 | 72 |

2 | 36 |

2 | 18 |

3 | 9 |

3 | 3 |

1 |

Prime factors of 72 are 2,3. Prime factorization of **72** in exponential form is:

72 = 2^{3}×3^{2}

∴ So by taking common prime factors GCF of 36 and 72 is 36

**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 72**

List of positive integer factors of 72 that divides 72 without a remainder.

1,2,3,4,6,8,9,12,18,24,36,72

**Greatest Common Factor**

We found the factors and prime factorization of 36 and 72. The biggest common factor number is the **GCF** number.

So the **greatest common factor 36 and 72** is **36**.

Also check out the Least Common Multiple of 36 and 72

(i) The GCF of 36 and 72 is associative

GCF of 36 and 72 = GCF of 72 and 36

1. What is the GCF of 36 and 72?

Answer: GCF of 36 and 72 is 36.

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 72?

Answer: Factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72. There are 12 integers that are factors of 72. The greatest factor of 72 is 72.

4. How to Find the GCF of 36 and 72?

Answer:

Greatest Common Factor of 36 and 72 = 36

Step 1: Find the prime factorization of 36

36 = 2 x 2 x 3 x 3

Step 2: Find the prime factorization of 72

72 = 2 x 2 x 2 x 3 x 3

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

GCF = 2 x 2 x 3 x 3 = 36

Step 4: Therefore, the greatest common factor of 36 and 72 is 36