Greatest Common Factor of 84 and 99
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 84, 99 i.e. 3 largest integer by which both the numbers can be divided.
Greatest common factor (GCF) of 84 and 99 is 3.
GCF(84,99) = 3
GCF of 84 and 99
Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;
- Greatest Common Factor of 84 and 99 by prime factorization method
- Greatest Common Factor of 84 and 99 by matching factors method
GCF of 84 and 99 is 3
Prime Factorization of 84
| 2 | 84 |
| 2 | 42 |
| 3 | 21 |
| 7 | 7 |
| 1 |
Prime factors of 84 are 2,3,7. Prime factorization of 84 in exponential form is:
84 = 22×31×71
Prime Factorization of 99
| 3 | 99 |
| 3 | 33 |
| 11 | 11 |
| 1 |
Prime factors of 99 are 3,11. Prime factorization of 99 in exponential form is:
99 = 32×111
∴ So by taking common prime factors GCF of 84 and 99 is 3
Greatest Common Factor of 84 and 99 by matching factors method
Factors of 84
List of positive integer factors of 84 that divides 84 without a remainder.
1,2,3,4,6,7,12,14,21,28,42,84
Factors of 99
List of positive integer factors of 99 that divides 99 without a remainder.
1,3,9,11,33,99
Greatest Common Factor
We found the factors and prime factorization of 84 and 99. The biggest common factor number is the GCF number.
So the greatest common factor 84 and 99 is 3.
Also check out the Least Common Multiple of 84 and 99
Properties of GCF 84 and 99
(i) The GCF of 84 and 99 is associative
GCF of 84 and 99 = GCF of 99 and 84
Related Greatest Common Factor of 84
Related Greatest Common Factor of 99
Frequently Asked Questions on GCF of 84 and 99
1. What is the GCF of 84 and 99?
Answer: GCF of 84 and 99 is 3.
2. What are the Factors of 84?
Answer: Factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84. There are 12 integers that are factors of 84. The greatest factor of 84 is 84.
3. What are the Factors of 99?
Answer: Factors of 99 are 1, 3, 9, 11, 33, 99. There are 6 integers that are factors of 99. The greatest factor of 99 is 99.
4. How to Find the GCF of 84 and 99?
Answer:
Greatest Common Factor of 84 and 99 = 3
Step 1: Find the prime factorization of 84
84 = 2 x 2 x 3 x 7
Step 2: Find the prime factorization of 99
99 = 3 x 3 x 11
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 84 and 99 is 3
