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 4214, 4216 i.e. 2 largest integer by which both the numbers can be divided.
Greatest common factor (GCF) of 4214 and 4216 is 2.
GCF(4214,4216) = 2
Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;
Prime Factorization of 4214
2 | 4214 |
7 | 2107 |
7 | 301 |
43 | 43 |
1 |
Prime factors of 4214 are 2,7,43. Prime factorization of 4214 in exponential form is:
4214 = 21×72×431
Prime Factorization of 4216
2 | 4216 |
2 | 2108 |
2 | 1054 |
17 | 527 |
31 | 31 |
1 |
Prime factors of 4216 are 2,17,31. Prime factorization of 4216 in exponential form is:
4216 = 23×171×311
∴ So by taking common prime factors GCF of 4214 and 4216 is 2
Factors of 4214
List of positive integer factors of 4214 that divides 4214 without a remainder.
1,2,7,14,43,49,86,98,301,602,2107,4214
Factors of 4216
List of positive integer factors of 4216 that divides 4216 without a remainder.
1,2,4,8,17,31,34,62,68,124,136,248,527,1054,2108,4216
Greatest Common Factor
We found the factors and prime factorization of 4214 and 4216. The biggest common factor number is the GCF number.
So the greatest common factor 4214 and 4216 is 2.
Also check out the Least Common Multiple of 4214 and 4216
(i) The GCF of 4214 and 4216 is associative
GCF of 4214 and 4216 = GCF of 4216 and 4214
1. What is the GCF of 4214 and 4216?
Answer: GCF of 4214 and 4216 is 2.
2. What are the Factors of 4214?
Answer: Factors of 4214 are 1, 2, 7, 14, 43, 49, 86, 98, 301, 602, 2107, 4214. There are 12 integers that are factors of 4214. The greatest factor of 4214 is 4214.
3. What are the Factors of 4216?
Answer: Factors of 4216 are 1, 2, 4, 8, 17, 31, 34, 62, 68, 124, 136, 248, 527, 1054, 2108, 4216. There are 16 integers that are factors of 4216. The greatest factor of 4216 is 4216.
4. How to Find the GCF of 4214 and 4216?
Answer:
Greatest Common Factor of 4214 and 4216 = 2
Step 1: Find the prime factorization of 4214
4214 = 2 x 7 x 7 x 43
Step 2: Find the prime factorization of 4216
4216 = 2 x 2 x 2 x 17 x 31
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 4214 and 4216 is 2