Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 34, 45 i.e. 1 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 34 and 45 is **1**.

GCF(34,45) = 1

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

- Greatest Common Factor of 34 and 45 by prime factorization method
- Greatest Common Factor of 34 and 45 by matching factors method

**Prime Factorization of 34**

2 | 34 |

17 | 17 |

1 |

Prime factors of 34 are 2,17. Prime factorization of **34** in exponential form is:

34 = 2^{1}×17^{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 34 and 45 is 1

**Factors of 34**

List of positive integer factors of 34 that divides 34 without a remainder.

1,2,17,34

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

So the **greatest common factor 34 and 45** is **1**.

Also check out the Least Common Multiple of 34 and 45

(i) The GCF of 34 and 45 is associative

GCF of 34 and 45 = GCF of 45 and 34

1. What is the GCF of 34 and 45?

Answer: GCF of 34 and 45 is 1.

2. What are the Factors of 34?

Answer: Factors of 34 are 1, 2, 17, 34. There are 4 integers that are factors of 34. The greatest factor of 34 is 34.

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 34 and 45?

Answer:

Greatest Common Factor of 34 and 45 = 1

Step 1: Find the prime factorization of 34

34 = 2 x 17

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 = = 1

Step 4: Therefore, the greatest common factor of 34 and 45 is 1