Greatest Common Factor of 106 and 114
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 106, 114 i.e. 2 largest integer by which both the numbers can be divided.
Greatest common factor (GCF) of 106 and 114 is 2.
GCF(106,114) = 2
GCF of 106 and 114
Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;
- Greatest Common Factor of 106 and 114 by prime factorization method
- Greatest Common Factor of 106 and 114 by matching factors method
GCF of 106 and 114 is 2
Prime Factorization of 106
| 2 | 106 |
| 53 | 53 |
| 1 |
Prime factors of 106 are 2,53. Prime factorization of 106 in exponential form is:
106 = 21×531
Prime Factorization of 114
| 2 | 114 |
| 3 | 57 |
| 19 | 19 |
| 1 |
Prime factors of 114 are 2,3,19. Prime factorization of 114 in exponential form is:
114 = 21×31×191
∴ So by taking common prime factors GCF of 106 and 114 is 2
Greatest Common Factor of 106 and 114 by matching factors method
Factors of 106
List of positive integer factors of 106 that divides 106 without a remainder.
1,2,53,106
Factors of 114
List of positive integer factors of 114 that divides 114 without a remainder.
1,2,3,6,19,38,57,114
Greatest Common Factor
We found the factors and prime factorization of 106 and 114. The biggest common factor number is the GCF number.
So the greatest common factor 106 and 114 is 2.
Also check out the Least Common Multiple of 106 and 114
Properties of GCF 106 and 114
(i) The GCF of 106 and 114 is associative
GCF of 106 and 114 = GCF of 114 and 106
Related Greatest Common Factor of 106
Related Greatest Common Factor of 114
Frequently Asked Questions on GCF of 106 and 114
1. What is the GCF of 106 and 114?
Answer: GCF of 106 and 114 is 2.
2. What are the Factors of 106?
Answer: Factors of 106 are 1, 2, 53, 106. There are 4 integers that are factors of 106. The greatest factor of 106 is 106.
3. What are the Factors of 114?
Answer: Factors of 114 are 1, 2, 3, 6, 19, 38, 57, 114. There are 8 integers that are factors of 114. The greatest factor of 114 is 114.
4. How to Find the GCF of 106 and 114?
Answer:
Greatest Common Factor of 106 and 114 = 2
Step 1: Find the prime factorization of 106
106 = 2 x 53
Step 2: Find the prime factorization of 114
114 = 2 x 3 x 19
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 106 and 114 is 2