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 10, 14 i.e. 2 largest integer by which both the numbers can be divided.
Greatest common factor (GCF) of 10 and 14 is 2.
GCF(10,14) = 2
Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;
Prime Factorization of 10
2 | 10 |
5 | 5 |
1 |
Prime factors of 10 are 2,5. Prime factorization of 10 in exponential form is:
10 = 21×51
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
∴ So by taking common prime factors GCF of 10 and 14 is 2
Factors of 10
List of positive integer factors of 10 that divides 10 without a remainder.
1,2,5,10
Factors of 14
List of positive integer factors of 14 that divides 14 without a remainder.
1,2,7,14
Greatest Common Factor
We found the factors and prime factorization of 10 and 14. The biggest common factor number is the GCF number.
So the greatest common factor 10 and 14 is 2.
Also check out the Least Common Multiple of 10 and 14
(i) The GCF of 10 and 14 is associative
GCF of 10 and 14 = GCF of 14 and 10
1. What is the GCF of 10 and 14?
Answer: GCF of 10 and 14 is 2.
2. What are the Factors of 10?
Answer: Factors of 10 are 1, 2, 5, 10. There are 4 integers that are factors of 10. The greatest factor of 10 is 10.
3. 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.
4. How to Find the GCF of 10 and 14?
Answer:
Greatest Common Factor of 10 and 14 = 2
Step 1: Find the prime factorization of 10
10 = 2 x 5
Step 2: Find the prime factorization of 14
14 = 2 x 7
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 10 and 14 is 2