What is the Greatest Common Factor of 22725 and 22734?

Greatest common factor (GCF) of 22725 and 22734 is 9.

GCF(22725,22734) = 9

We will now calculate the prime factors of 22725 and 22734, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 22725 and 22734.

How to find the GCF of 22725 and 22734?

We will first find the prime factorization of 22725 and 22734. After we will calculate the factors of 22725 and 22734 and find the biggest common factor number .

Step-1: Prime Factorization of 22725

Prime factors of 22725 are 3, 5, 101. Prime factorization of 22725 in exponential form is:

22725 = 3² × 5² × 101¹

Step-2: 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-3: Factors of 22725

List of positive integer factors of 22725 that divides 22725 without a remainder.

1, 3, 5, 9, 15, 25, 45, 75, 101, 225, 303, 505, 909, 1515, 2525, 4545, 7575

Step-4: Factors of 22734

List of positive integer factors of 22734 that divides 22725 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 22725 and 22734. The biggest common factor number is the GCF number.
So the greatest common factor 22725 and 22734 is 9.

Also check out the Least Common Multiple of 22725 and 22734