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 90, 96 i.e. 6 largest integer by which both the numbers can be divided.
Greatest common factor (GCF) of 90 and 96 is 6.
GCF(90,96) = 6
Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;
Prime Factorization of 90
2 | 90 |
3 | 45 |
3 | 15 |
5 | 5 |
1 |
Prime factors of 90 are 2,3,5. Prime factorization of 90 in exponential form is:
90 = 21×32×51
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
∴ So by taking common prime factors GCF of 90 and 96 is 6
Factors of 90
List of positive integer factors of 90 that divides 90 without a remainder.
1,2,3,5,6,9,10,15,18,30,45,90
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
Greatest Common Factor
We found the factors and prime factorization of 90 and 96. The biggest common factor number is the GCF number.
So the greatest common factor 90 and 96 is 6.
Also check out the Least Common Multiple of 90 and 96
(i) The GCF of 90 and 96 is associative
GCF of 90 and 96 = GCF of 96 and 90
1. What is the GCF of 90 and 96?
Answer: GCF of 90 and 96 is 6.
2. What are the Factors of 90?
Answer: Factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90. There are 12 integers that are factors of 90. The greatest factor of 90 is 90.
3. 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.
4. How to Find the GCF of 90 and 96?
Answer:
Greatest Common Factor of 90 and 96 = 6
Step 1: Find the prime factorization of 90
90 = 2 x 3 x 3 x 5
Step 2: Find the prime factorization of 96
96 = 2 x 2 x 2 x 2 x 2 x 3
Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:
GCF = 2 x 3 = 6
Step 4: Therefore, the greatest common factor of 90 and 96 is 6