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, 30 i.e. 2 largest integer by which both the numbers can be divided.
Greatest common factor (GCF) of 14 and 30 is 2.
GCF(14,30) = 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 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 = 21×31×51
∴ So by taking common prime factors GCF of 14 and 30 is 2
Factors of 14
List of positive integer factors of 14 that divides 14 without a remainder.
1,2,7,14
Factors of 30
List of positive integer factors of 30 that divides 30 without a remainder.
1,2,3,5,6,10,15,30
Greatest Common Factor
We found the factors and prime factorization of 14 and 30. The biggest common factor number is the GCF number.
So the greatest common factor 14 and 30 is 2.
Also check out the Least Common Multiple of 14 and 30
(i) The GCF of 14 and 30 is associative
GCF of 14 and 30 = GCF of 30 and 14
1. What is the GCF of 14 and 30?
Answer: GCF of 14 and 30 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 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.
4. How to Find the GCF of 14 and 30?
Answer:
Greatest Common Factor of 14 and 30 = 2
Step 1: Find the prime factorization of 14
14 = 2 x 7
Step 2: Find the prime factorization of 30
30 = 2 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 = 2
Step 4: Therefore, the greatest common factor of 14 and 30 is 2