What is the Greatest Common Factor of 22100 and 22117?

Greatest common factor (GCF) of 22100 and 22117 is 17.

GCF(22100,22117) = 17

We will now calculate the prime factors of 22100 and 22117, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 22100 and 22117.

How to find the GCF of 22100 and 22117?

We will first find the prime factorization of 22100 and 22117. After we will calculate the factors of 22100 and 22117 and find the biggest common factor number .

Step-1: Prime Factorization of 22100

Prime factors of 22100 are 2, 5, 13, 17. Prime factorization of 22100 in exponential form is:

22100 = 2² × 5² × 13¹ × 17¹

Step-2: Prime Factorization of 22117

Prime factors of 22117 are 17, 1301. Prime factorization of 22117 in exponential form is:

22117 = 17¹ × 1301¹

Step-3: Factors of 22100

List of positive integer factors of 22100 that divides 22100 without a remainder.

1, 2, 4, 5, 10, 13, 17, 20, 25, 26, 34, 50, 52, 65, 68, 85, 100, 130, 170, 221, 260, 325, 340, 425, 442, 650, 850, 884, 1105, 1300, 1700, 2210, 4420, 5525, 11050

Step-4: Factors of 22117

List of positive integer factors of 22117 that divides 22100 without a remainder.

1, 17, 1301

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 22100 and 22117. The biggest common factor number is the GCF number.
So the greatest common factor 22100 and 22117 is 17.

Also check out the Least Common Multiple of 22100 and 22117