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 96, 109 i.e. 1 largest integer by which both the numbers can be divided.
Greatest common factor (GCF) of 96 and 109 is 1.
GCF(96,109) = 1
Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;
Prime Factorization of 96
2 | 96 |
2 | 48 |
2 | 24 |
2 | 12 |
2 | 6 |
3 | 3 |
1 |
Prime factors of 96 are 2,3. Prime factorization of 96 in exponential form is:
96 = 25×31
Prime Factorization of 109
109 | 109 |
1 |
Prime factors of 109 are 109. Prime factorization of 109 in exponential form is:
109 = 1091
∴ So by taking common prime factors GCF of 96 and 109 is 1
Factors of 96
List of positive integer factors of 96 that divides 96 without a remainder.
1,2,3,4,6,8,12,16,24,32,48,96
Factors of 109
List of positive integer factors of 109 that divides 109 without a remainder.
1,109
Greatest Common Factor
We found the factors and prime factorization of 96 and 109. The biggest common factor number is the GCF number.
So the greatest common factor 96 and 109 is 1.
Also check out the Least Common Multiple of 96 and 109
(i) The GCF of 96 and 109 is associative
GCF of 96 and 109 = GCF of 109 and 96
1. What is the GCF of 96 and 109?
Answer: GCF of 96 and 109 is 1.
2. What are the Factors of 96?
Answer: Factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96. There are 12 integers that are factors of 96. The greatest factor of 96 is 96.
3. What are the Factors of 109?
Answer: Factors of 109 are 1, 109. There are 2 integers that are factors of 109. The greatest factor of 109 is 109.
4. How to Find the GCF of 96 and 109?
Answer:
Greatest Common Factor of 96 and 109 = 1
Step 1: Find the prime factorization of 96
96 = 2 x 2 x 2 x 2 x 2 x 3
Step 2: Find the prime factorization of 109
109 = 109
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 96 and 109 is 1