Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
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;
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 = 21×171
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 = 32×51
∴ 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