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 2202, 2205 i.e. 3 largest integer by which both the numbers can be divided.
Greatest common factor (GCF) of 2202 and 2205 is 3.
GCF(2202,2205) = 3
Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;
Prime Factorization of 2202
2 | 2202 |
3 | 1101 |
367 | 367 |
1 |
Prime factors of 2202 are 2,3,367. Prime factorization of 2202 in exponential form is:
2202 = 21×31×3671
Prime Factorization of 2205
3 | 2205 |
3 | 735 |
5 | 245 |
7 | 49 |
7 | 7 |
1 |
Prime factors of 2205 are 3,5,7. Prime factorization of 2205 in exponential form is:
2205 = 32×51×72
∴ So by taking common prime factors GCF of 2202 and 2205 is 3
Factors of 2202
List of positive integer factors of 2202 that divides 2202 without a remainder.
1,2,3,6,367,734,1101,2202
Factors of 2205
List of positive integer factors of 2205 that divides 2205 without a remainder.
1,3,5,7,9,15,21,35,45,49,63,105,147,245,315,441,735,2205
Greatest Common Factor
We found the factors and prime factorization of 2202 and 2205. The biggest common factor number is the GCF number.
So the greatest common factor 2202 and 2205 is 3.
Also check out the Least Common Multiple of 2202 and 2205
(i) The GCF of 2202 and 2205 is associative
GCF of 2202 and 2205 = GCF of 2205 and 2202
1. What is the GCF of 2202 and 2205?
Answer: GCF of 2202 and 2205 is 3.
2. What are the Factors of 2202?
Answer: Factors of 2202 are 1, 2, 3, 6, 367, 734, 1101, 2202. There are 8 integers that are factors of 2202. The greatest factor of 2202 is 2202.
3. What are the Factors of 2205?
Answer: Factors of 2205 are 1, 3, 5, 7, 9, 15, 21, 35, 45, 49, 63, 105, 147, 245, 315, 441, 735, 2205. There are 18 integers that are factors of 2205. The greatest factor of 2205 is 2205.
4. How to Find the GCF of 2202 and 2205?
Answer:
Greatest Common Factor of 2202 and 2205 = 3
Step 1: Find the prime factorization of 2202
2202 = 2 x 3 x 367
Step 2: Find the prime factorization of 2205
2205 = 3 x 3 x 5 x 7 x 7
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 2202 and 2205 is 3