Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 35, 45 i.e. 5 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 35 and 45 is **5**.

GCF(35,45) = 5

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

- Greatest Common Factor of 35 and 45 by prime factorization method
- Greatest Common Factor of 35 and 45 by matching factors method

**Prime Factorization of 35**

5 | 35 |

7 | 7 |

1 |

Prime factors of 35 are 5,7. Prime factorization of **35** in exponential form is:

35 = 5^{1}×7^{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 35 and 45 is 5

**Factors of 35**

List of positive integer factors of 35 that divides 35 without a remainder.

1,5,7,35

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

So the **greatest common factor 35 and 45** is **5**.

Also check out the Least Common Multiple of 35 and 45

(i) The GCF of 35 and 45 is associative

GCF of 35 and 45 = GCF of 45 and 35

1. What is the GCF of 35 and 45?

Answer: GCF of 35 and 45 is 5.

2. What are the Factors of 35?

Answer: Factors of 35 are 1, 5, 7, 35. There are 4 integers that are factors of 35. The greatest factor of 35 is 35.

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 35 and 45?

Answer:

Greatest Common Factor of 35 and 45 = 5

Step 1: Find the prime factorization of 35

35 = 5 x 7

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 = 5

Step 4: Therefore, the greatest common factor of 35 and 45 is 5