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 203, 208 i.e. 1 largest integer by which both the numbers can be divided.
Greatest common factor (GCF) of 203 and 208 is 1.
GCF(203,208) = 1
Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;
Prime Factorization of 203
7 | 203 |
29 | 29 |
1 |
Prime factors of 203 are 7,29. Prime factorization of 203 in exponential form is:
203 = 71×291
Prime Factorization of 208
2 | 208 |
2 | 104 |
2 | 52 |
2 | 26 |
13 | 13 |
1 |
Prime factors of 208 are 2,13. Prime factorization of 208 in exponential form is:
208 = 24×131
∴ So by taking common prime factors GCF of 203 and 208 is 1
Factors of 203
List of positive integer factors of 203 that divides 203 without a remainder.
1,7,29,203
Factors of 208
List of positive integer factors of 208 that divides 208 without a remainder.
1,2,4,8,13,16,26,52,104,208
Greatest Common Factor
We found the factors and prime factorization of 203 and 208. The biggest common factor number is the GCF number.
So the greatest common factor 203 and 208 is 1.
Also check out the Least Common Multiple of 203 and 208
(i) The GCF of 203 and 208 is associative
GCF of 203 and 208 = GCF of 208 and 203
1. What is the GCF of 203 and 208?
Answer: GCF of 203 and 208 is 1.
2. What are the Factors of 203?
Answer: Factors of 203 are 1, 7, 29, 203. There are 4 integers that are factors of 203. The greatest factor of 203 is 203.
3. What are the Factors of 208?
Answer: Factors of 208 are 1, 2, 4, 8, 13, 16, 26, 52, 104, 208. There are 10 integers that are factors of 208. The greatest factor of 208 is 208.
4. How to Find the GCF of 203 and 208?
Answer:
Greatest Common Factor of 203 and 208 = 1
Step 1: Find the prime factorization of 203
203 = 7 x 29
Step 2: Find the prime factorization of 208
208 = 2 x 2 x 2 x 2 x 13
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 203 and 208 is 1