What is the Greatest Common Factor of 22734 and 22749?

Greatest common factor (GCF) of 22734 and 22749 is 3.

GCF(22734,22749) = 3

We will now calculate the prime factors of 22734 and 22749, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 22734 and 22749.

How to find the GCF of 22734 and 22749?

We will first find the prime factorization of 22734 and 22749. After we will calculate the factors of 22734 and 22749 and find the biggest common factor number .

Step-1: Prime Factorization of 22734

Prime factors of 22734 are 2, 3, 421. Prime factorization of 22734 in exponential form is:

22734 = 2¹ × 3³ × 421¹

Step-2: Prime Factorization of 22749

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

22749 = 3¹ × 7583¹

Step-3: Factors of 22734

List of positive integer factors of 22734 that divides 22734 without a remainder.

1, 2, 3, 6, 9, 18, 27, 54, 421, 842, 1263, 2526, 3789, 7578, 11367

Step-4: Factors of 22749

List of positive integer factors of 22749 that divides 22734 without a remainder.

1, 3, 7583

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 22734 and 22749. The biggest common factor number is the GCF number.
So the greatest common factor 22734 and 22749 is 3.

Also check out the Least Common Multiple of 22734 and 22749