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 64, 84 i.e. 4 largest integer by which both the numbers can be divided.
Greatest common factor (GCF) of 64 and 84 is 4.
GCF(64,84) = 4
Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;
Prime Factorization of 64
2 | 64 |
2 | 32 |
2 | 16 |
2 | 8 |
2 | 4 |
2 | 2 |
1 |
Prime factors of 64 are 2. Prime factorization of 64 in exponential form is:
64 = 26
Prime Factorization of 84
2 | 84 |
2 | 42 |
3 | 21 |
7 | 7 |
1 |
Prime factors of 84 are 2.Prime factorization of 84 in exponential form is:
84 = 22×31×71
∴ So by taking common prime factors GCF of 64 and 84 is 4
Factors of 64
List of positive integer factors of 64 that divides 64 without a remainder.
1,2,4,8,16,32,64
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
Greatest Common Factor
We found the factors and prime factorization of 64 and 84. The biggest common factor number is the GCF number.
So the greatest common factor 64 and 84 is 4.
Also check out the Least Common Multiple of 64 and 84
(i) The GCF of 64 and 84 is associative
GCF of 64 and 84 = GCF of 84 and 64
1. What is the GCF of 64 and 84?
Answer: GCF of 64 and 84 is 4.
2. What are the Factors of 64?
Answer: Factors of 64 are 1, 2, 4, 8, 16, 32, 64. There are 7 integers that are factors of 64. The greatest factor of 64 is 64.
3. 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.
4. How to Find the GCF of 64 and 84?
Answer:
Greatest Common Factor of 64 and 84 = 4
Step 1: Find the prime factorization of 64
64 = 2 x 2 x 2 x 2 x 2 x 2
Step 2: Find the prime factorization of 84
84 = 2 x 2 x 3 x 7
Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:
GCF = 2 x 2 = 4
Step 4: Therefore, the greatest common factor of 64 and 84 is 4