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