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 14, 34 i.e. 2 largest integer by which both the numbers can be divided.
Greatest common factor (GCF) of 14 and 34 is 2.
GCF(14,34) = 2
Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;
Prime Factorization of 14
2 | 14 |
7 | 7 |
1 |
Prime factors of 14 are 2,7. Prime factorization of 14 in exponential form is:
14 = 21×71
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
∴ So by taking common prime factors GCF of 14 and 34 is 2
Factors of 14
List of positive integer factors of 14 that divides 14 without a remainder.
1,2,7,14
Factors of 34
List of positive integer factors of 34 that divides 34 without a remainder.
1,2,17,34
Greatest Common Factor
We found the factors and prime factorization of 14 and 34. The biggest common factor number is the GCF number.
So the greatest common factor 14 and 34 is 2.
Also check out the Least Common Multiple of 14 and 34
(i) The GCF of 14 and 34 is associative
GCF of 14 and 34 = GCF of 34 and 14
1. What is the GCF of 14 and 34?
Answer: GCF of 14 and 34 is 2.
2. What are the Factors of 14?
Answer: Factors of 14 are 1, 2, 7, 14. There are 4 integers that are factors of 14. The greatest factor of 14 is 14.
3. 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.
4. How to Find the GCF of 14 and 34?
Answer:
Greatest Common Factor of 14 and 34 = 2
Step 1: Find the prime factorization of 14
14 = 2 x 7
Step 2: Find the prime factorization of 34
34 = 2 x 17
Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:
GCF = 2
Step 4: Therefore, the greatest common factor of 14 and 34 is 2