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 8214, 8216 i.e. 2 largest integer by which both the numbers can be divided.
Greatest common factor (GCF) of 8214 and 8216 is 2.
GCF(8214,8216) = 2
Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;
Prime Factorization of 8214
2 | 8214 |
3 | 4107 |
37 | 1369 |
37 | 37 |
1 |
Prime factors of 8214 are 2,3,37. Prime factorization of 8214 in exponential form is:
8214 = 21×31×372
Prime Factorization of 8216
2 | 8216 |
2 | 4108 |
2 | 2054 |
13 | 1027 |
79 | 79 |
1 |
Prime factors of 8216 are 2,13,79. Prime factorization of 8216 in exponential form is:
8216 = 23×131×791
∴ So by taking common prime factors GCF of 8214 and 8216 is 2
Factors of 8214
List of positive integer factors of 8214 that divides 8214 without a remainder.
1,2,3,6,37,74,111,222,1369,2738,4107,8214
Factors of 8216
List of positive integer factors of 8216 that divides 8216 without a remainder.
1,2,4,8,13,26,52,79,104,158,316,632,1027,2054,4108,8216
Greatest Common Factor
We found the factors and prime factorization of 8214 and 8216. The biggest common factor number is the GCF number.
So the greatest common factor 8214 and 8216 is 2.
Also check out the Least Common Multiple of 8214 and 8216
(i) The GCF of 8214 and 8216 is associative
GCF of 8214 and 8216 = GCF of 8216 and 8214
1. What is the GCF of 8214 and 8216?
Answer: GCF of 8214 and 8216 is 2.
2. What are the Factors of 8214?
Answer: Factors of 8214 are 1, 2, 3, 6, 37, 74, 111, 222, 1369, 2738, 4107, 8214. There are 12 integers that are factors of 8214. The greatest factor of 8214 is 8214.
3. What are the Factors of 8216?
Answer: Factors of 8216 are 1, 2, 4, 8, 13, 26, 52, 79, 104, 158, 316, 632, 1027, 2054, 4108, 8216. There are 16 integers that are factors of 8216. The greatest factor of 8216 is 8216.
4. How to Find the GCF of 8214 and 8216?
Answer:
Greatest Common Factor of 8214 and 8216 = 2
Step 1: Find the prime factorization of 8214
8214 = 2 x 3 x 37 x 37
Step 2: Find the prime factorization of 8216
8216 = 2 x 2 x 2 x 13 x 79
Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:
GCF = 2
Step 4: Therefore, the greatest common factor of 8214 and 8216 is 2