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 8, 21 i.e. 1 largest integer by which both the numbers can be divided.
Greatest common factor (GCF) of 8 and 21 is 1.
GCF(8,21) = 1
Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;
Prime Factorization of 8
2 | 8 |
2 | 4 |
2 | 2 |
1 |
Prime factors of 8 are 2. Prime factorization of 8 in exponential form is:
8 = 23
Prime Factorization of 21
3 | 21 |
7 | 7 |
1 |
Prime factors of 21 are 3.Prime factorization of 21 in exponential form is:
21 = 31×71
∴ So by taking common prime factors GCF of 8 and 21 is 1
Factors of 8
List of positive integer factors of 8 that divides 8 without a remainder.
1,2,4,8
Factors of 21
List of positive integer factors of 21 that divides 21 without a remainder.
1,3,7,21
Greatest Common Factor
We found the factors and prime factorization of 8 and 21. The biggest common factor number is the GCF number.
So the greatest common factor 8 and 21 is 1.
Also check out the Least Common Multiple of 8 and 21
(i) The GCF of 8 and 21 is associative
GCF of 8 and 21 = GCF of 21 and 8
1. What is the GCF of 8 and 21?
Answer: GCF of 8 and 21 is 1.
2. What are the Factors of 8?
Answer: Factors of 8 are 1, 2, 4, 8. There are 4 integers that are factors of 8. The greatest factor of 8 is 8.
3. What are the Factors of 21?
Answer: Factors of 21 are 1, 3, 7, 21. There are 4 integers that are factors of 21. The greatest factor of 21 is 21.
4. How to Find the GCF of 8 and 21?
Answer:
Greatest Common Factor of 8 and 21 = 1
Step 1: Find the prime factorization of 8
8 = 2 x 2 x 2
Step 2: Find the prime factorization of 21
21 = 3 x 7
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 8 and 21 is 1