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 216, 217 i.e. 1 largest integer by which both the numbers can be divided.
Greatest common factor (GCF) of 216 and 217 is 1.
GCF(216,217) = 1
Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;
Prime Factorization of 216
2 | 216 |
2 | 108 |
2 | 54 |
3 | 27 |
3 | 9 |
3 | 3 |
1 |
Prime factors of 216 are 2,3. Prime factorization of 216 in exponential form is:
216 = 23×33
Prime Factorization of 217
7 | 217 |
31 | 31 |
1 |
Prime factors of 217 are 7,31. Prime factorization of 217 in exponential form is:
217 = 71×311
∴ So by taking common prime factors GCF of 216 and 217 is 1
Factors of 216
List of positive integer factors of 216 that divides 216 without a remainder.
1,2,3,4,6,8,9,12,18,24,27,36,54,72,108,216
Factors of 217
List of positive integer factors of 217 that divides 217 without a remainder.
1,7,31,217
Greatest Common Factor
We found the factors and prime factorization of 216 and 217. The biggest common factor number is the GCF number.
So the greatest common factor 216 and 217 is 1.
Also check out the Least Common Multiple of 216 and 217
(i) The GCF of 216 and 217 is associative
GCF of 216 and 217 = GCF of 217 and 216
1. What is the GCF of 216 and 217?
Answer: GCF of 216 and 217 is 1.
2. What are the Factors of 216?
Answer: Factors of 216 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216. There are 16 integers that are factors of 216. The greatest factor of 216 is 216.
3. What are the Factors of 217?
Answer: Factors of 217 are 1, 7, 31, 217. There are 4 integers that are factors of 217. The greatest factor of 217 is 217.
4. How to Find the GCF of 216 and 217?
Answer:
Greatest Common Factor of 216 and 217 = 1
Step 1: Find the prime factorization of 216
216 = 2 x 2 x 2 x 3 x 3 x 3
Step 2: Find the prime factorization of 217
217 = 7 x 31
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 216 and 217 is 1