What is the Greatest Common Factor of 22083 and 22100?

Greatest common factor (GCF) of 22083 and 22100 is 17.

GCF(22083,22100) = 17

We will now calculate the prime factors of 22083 and 22100, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 22083 and 22100.

How to find the GCF of 22083 and 22100?

We will first find the prime factorization of 22083 and 22100. After we will calculate the factors of 22083 and 22100 and find the biggest common factor number .

Step-1: Prime Factorization of 22083

Prime factors of 22083 are 3, 17, 433. Prime factorization of 22083 in exponential form is:

22083 = 3¹ × 17¹ × 433¹

Step-2: 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-3: Factors of 22083

List of positive integer factors of 22083 that divides 22083 without a remainder.

1, 3, 17, 51, 433, 1299, 7361

Step-4: Factors of 22100

List of positive integer factors of 22100 that divides 22083 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 22083 and 22100. The biggest common factor number is the GCF number.
So the greatest common factor 22083 and 22100 is 17.

Also check out the Least Common Multiple of 22083 and 22100