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 2102, 2109 i.e. 1 largest integer by which both the numbers can be divided.
Greatest common factor (GCF) of 2102 and 2109 is 1.
GCF(2102,2109) = 1
Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;
Prime Factorization of 2102
2 | 2102 |
1051 | 1051 |
1 |
Prime factors of 2102 are 2,1051. Prime factorization of 2102 in exponential form is:
2102 = 21×10511
Prime Factorization of 2109
3 | 2109 |
19 | 703 |
37 | 37 |
1 |
Prime factors of 2109 are 3,19,37. Prime factorization of 2109 in exponential form is:
2109 = 31×191×371
∴ So by taking common prime factors GCF of 2102 and 2109 is 1
Factors of 2102
List of positive integer factors of 2102 that divides 2102 without a remainder.
1,2,1051,2102
Factors of 2109
List of positive integer factors of 2109 that divides 2109 without a remainder.
1,3,19,37,57,111,703,2109
Greatest Common Factor
We found the factors and prime factorization of 2102 and 2109. The biggest common factor number is the GCF number.
So the greatest common factor 2102 and 2109 is 1.
Also check out the Least Common Multiple of 2102 and 2109
(i) The GCF of 2102 and 2109 is associative
GCF of 2102 and 2109 = GCF of 2109 and 2102
1. What is the GCF of 2102 and 2109?
Answer: GCF of 2102 and 2109 is 1.
2. What are the Factors of 2102?
Answer: Factors of 2102 are 1, 2, 1051, 2102. There are 4 integers that are factors of 2102. The greatest factor of 2102 is 2102.
3. What are the Factors of 2109?
Answer: Factors of 2109 are 1, 3, 19, 37, 57, 111, 703, 2109. There are 8 integers that are factors of 2109. The greatest factor of 2109 is 2109.
4. How to Find the GCF of 2102 and 2109?
Answer:
Greatest Common Factor of 2102 and 2109 = 1
Step 1: Find the prime factorization of 2102
2102 = 2 x 1051
Step 2: Find the prime factorization of 2109
2109 = 3 x 19 x 37
Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:
GCF = = 1
Step 4: Therefore, the greatest common factor of 2102 and 2109 is 1