Greatest Common Factor of 123 and 129
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 123, 129 i.e. 3 largest integer by which both the numbers can be divided.
Greatest common factor (GCF) of 123 and 129 is 3.
GCF(123,129) = 3
GCF of 123 and 129
Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;
- Greatest Common Factor of 123 and 129 by prime factorization method
- Greatest Common Factor of 123 and 129 by matching factors method
GCF of 123 and 129 is 3
Prime Factorization of 123
| 3 | 123 |
| 41 | 41 |
| 1 |
Prime factors of 123 are 3,41. Prime factorization of 123 in exponential form is:
123 = 31×411
Prime Factorization of 129
| 3 | 129 |
| 43 | 43 |
| 1 |
Prime factors of 129 are 3,43. Prime factorization of 129 in exponential form is:
129 = 31×431
∴ So by taking common prime factors GCF of 123 and 129 is 3
Greatest Common Factor of 123 and 129 by matching factors method
Factors of 123
List of positive integer factors of 123 that divides 123 without a remainder.
1,3,41,123
Factors of 129
List of positive integer factors of 129 that divides 129 without a remainder.
1,3,43,129
Greatest Common Factor
We found the factors and prime factorization of 123 and 129. The biggest common factor number is the GCF number.
So the greatest common factor 123 and 129 is 3.
Also check out the Least Common Multiple of 123 and 129
Properties of GCF 123 and 129
(i) The GCF of 123 and 129 is associative
GCF of 123 and 129 = GCF of 129 and 123
Related Greatest Common Factor of 123
Related Greatest Common Factor of 129
Frequently Asked Questions on GCF of 123 and 129
1. What is the GCF of 123 and 129?
Answer: GCF of 123 and 129 is 3.
2. What are the Factors of 123?
Answer: Factors of 123 are 1, 3, 41, 123. There are 4 integers that are factors of 123. The greatest factor of 123 is 123.
3. What are the Factors of 129?
Answer: Factors of 129 are 1, 3, 43, 129. There are 4 integers that are factors of 129. The greatest factor of 129 is 129.
4. How to Find the GCF of 123 and 129?
Answer:
Greatest Common Factor of 123 and 129 = 3
Step 1: Find the prime factorization of 123
123 = 3 x 41
Step 2: Find the prime factorization of 129
129 = 3 x 43
Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:
GCF = 3
Step 4: Therefore, the greatest common factor of 123 and 129 is 3