What is the Greatest Common Factor of 22749 and 22755?

Greatest common factor (GCF) of 22749 and 22755 is 3.

GCF(22749,22755) = 3

We will now calculate the prime factors of 22749 and 22755, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 22749 and 22755.

How to find the GCF of 22749 and 22755?

We will first find the prime factorization of 22749 and 22755. After we will calculate the factors of 22749 and 22755 and find the biggest common factor number .

Step-1: Prime Factorization of 22749

Prime factors of 22749 are 3, 7583. Prime factorization of 22749 in exponential form is:

22749 = 3¹ × 7583¹

Step-2: Prime Factorization of 22755

Prime factors of 22755 are 3, 5, 37, 41. Prime factorization of 22755 in exponential form is:

22755 = 3¹ × 5¹ × 37¹ × 41¹

Step-3: Factors of 22749

List of positive integer factors of 22749 that divides 22749 without a remainder.

1, 3, 7583

Step-4: Factors of 22755

List of positive integer factors of 22755 that divides 22749 without a remainder.

1, 3, 5, 15, 37, 41, 111, 123, 185, 205, 555, 615, 1517, 4551, 7585

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 22749 and 22755. The biggest common factor number is the GCF number.
So the greatest common factor 22749 and 22755 is 3.

Also check out the Least Common Multiple of 22749 and 22755