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, 100 i.e. 4 largest integer by which both the numbers can be divided.
Greatest common factor (GCF) of 84 and 100 is 4.
GCF(84,100) = 4
Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;
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 100
2 | 100 |
2 | 50 |
5 | 25 |
5 | 5 |
1 |
Prime factors of 100 are 2,5. Prime factorization of 100 in exponential form is:
100 = 22×52
∴ So by taking common prime factors GCF of 84 and 100 is 4
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 100
List of positive integer factors of 100 that divides 100 without a remainder.
1,2,4,5,10,20,25,50,100
Greatest Common Factor
We found the factors and prime factorization of 84 and 100. The biggest common factor number is the GCF number.
So the greatest common factor 84 and 100 is 4.
Also check out the Least Common Multiple of 84 and 100
(i) The GCF of 84 and 100 is associative
GCF of 84 and 100 = GCF of 100 and 84
1. What is the GCF of 84 and 100?
Answer: GCF of 84 and 100 is 4.
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 100?
Answer: Factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, 100. There are 9 integers that are factors of 100. The greatest factor of 100 is 100.
4. How to Find the GCF of 84 and 100?
Answer:
Greatest Common Factor of 84 and 100 = 4
Step 1: Find the prime factorization of 84
84 = 2 x 2 x 3 x 7
Step 2: Find the prime factorization of 100
100 = 2 x 2 x 5 x 5
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 84 and 100 is 4