Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 45, 30 i.e. 15 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 45 and 30 is **15**.

GCF(45,30) = 15

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

- Greatest Common Factor of 45 and 30 by prime factorization method
- Greatest Common Factor of 45 and 30 by matching factors method

**Prime Factorization of 30**

2 | 30 |

3 | 15 |

5 | 5 |

1 |

Prime factors of 30 are 2,3,5. Prime factorization of **30** in exponential form is:

30 = 2^{1}×3^{1}×5^{1}

**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 30 and 45 is 15

**Factors of 30**

List of positive integer factors of 30 that divides 30 without a remainder.

1,2,3,5,6,10,15,30

**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 30 and 45. The biggest common factor number is the **GCF** number.

So the **greatest common factor 30 and 45** is **15**.

Also check out the Least Common Multiple of 30 and 45

(i) The GCF of 30 and 45 is associative

GCF of 30 and 45 = GCF of 45 and 30

1. What is the GCF of 30 and 45?

Answer: GCF of 30 and 45 is 15.

2. What are the Factors of 30?

Answer: Factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30. There are 8 integers that are factors of 30. The greatest factor of 30 is 30.

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 30 and 45?

Answer:

Greatest Common Factor of 30 and 45 = 15

Step 1: Find the prime factorization of 30

30 = 2 x 3 x 5

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 5 = 15

Step 4: Therefore, the greatest common factor of 30 and 45 is 15