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 315, 321 i.e. 3 largest integer by which both the numbers can be divided.
Greatest common factor (GCF) of 315 and 321 is 3.
GCF(315,321) = 3
Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;
Prime Factorization of 315
3 | 315 |
3 | 105 |
5 | 35 |
7 | 7 |
1 |
Prime factors of 315 are 3,5,7. Prime factorization of 315 in exponential form is:
315 = 32×51×71
Prime Factorization of 321
3 | 321 |
107 | 107 |
1 |
Prime factors of 321 are 3,107. Prime factorization of 321 in exponential form is:
321 = 31×1071
∴ So by taking common prime factors GCF of 315 and 321 is 3
Factors of 315
List of positive integer factors of 315 that divides 315 without a remainder.
1,3,5,7,9,15,21,35,45,63,105,315
Factors of 321
List of positive integer factors of 321 that divides 321 without a remainder.
1,3,107,321
Greatest Common Factor
We found the factors and prime factorization of 315 and 321. The biggest common factor number is the GCF number.
So the greatest common factor 315 and 321 is 3.
Also check out the Least Common Multiple of 315 and 321
(i) The GCF of 315 and 321 is associative
GCF of 315 and 321 = GCF of 321 and 315
1. What is the GCF of 315 and 321?
Answer: GCF of 315 and 321 is 3.
2. What are the Factors of 315?
Answer: Factors of 315 are 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315. There are 12 integers that are factors of 315. The greatest factor of 315 is 315.
3. What are the Factors of 321?
Answer: Factors of 321 are 1, 3, 107, 321. There are 4 integers that are factors of 321. The greatest factor of 321 is 321.
4. How to Find the GCF of 315 and 321?
Answer:
Greatest Common Factor of 315 and 321 = 3
Step 1: Find the prime factorization of 315
315 = 3 x 3 x 5 x 7
Step 2: Find the prime factorization of 321
321 = 3 x 107
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 315 and 321 is 3