Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 36, 45 i.e. 9 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 36 and 45 is **9**.

GCF(36,45) = 9

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

- Greatest Common Factor of 36 and 45 by prime factorization method
- Greatest Common Factor of 36 and 45 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 45**

3 | 45 |

3 | 15 |

5 | 5 |

1 |

Prime factors of 45 are 3,5. Prime factorization of **45** in exponential form is:

45 = 3^{2}×5^{1}

∴ So by taking common prime factors GCF of 36 and 45 is 9

**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 45**

List of positive integer factors of 45 that divides 45 without a remainder.

1,3,5,9,15,45

**Greatest Common Factor**

We found the factors and prime factorization of 36 and 45. The biggest common factor number is the **GCF** number.

So the **greatest common factor 36 and 45** is **9**.

Also check out the Least Common Multiple of 36 and 45

(i) The GCF of 36 and 45 is associative

GCF of 36 and 45 = GCF of 45 and 36

1. What is the GCF of 36 and 45?

Answer: GCF of 36 and 45 is 9.

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 45?

Answer: Factors of 45 are 1, 3, 5, 9, 15, 45. There are 6 integers that are factors of 45. The greatest factor of 45 is 45.

4. How to Find the GCF of 36 and 45?

Answer:

Greatest Common Factor of 36 and 45 = 9

Step 1: Find the prime factorization of 36

36 = 2 x 2 x 3 x 3

Step 2: Find the prime factorization of 45

45 = 3 x 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 x 3 = 9

Step 4: Therefore, the greatest common factor of 36 and 45 is 9