What is the Greatest Common Factor of 75123 and 75135?

Greatest common factor (GCF) of 75123 and 75135 is 3.

GCF(75123,75135) = 3

We will now calculate the prime factors of 75123 and 75135, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75123 and 75135.

How to find the GCF of 75123 and 75135?

We will first find the prime factorization of 75123 and 75135. After we will calculate the factors of 75123 and 75135 and find the biggest common factor number .

Step-1: Prime Factorization of 75123

Prime factors of 75123 are 3, 17, 491. Prime factorization of 75123 in exponential form is:

75123 = 3² × 17¹ × 491¹

Step-2: Prime Factorization of 75135

Prime factors of 75135 are 3, 5, 5009. Prime factorization of 75135 in exponential form is:

75135 = 3¹ × 5¹ × 5009¹

Step-3: Factors of 75123

List of positive integer factors of 75123 that divides 75123 without a remainder.

1, 3, 9, 17, 51, 153, 491, 1473, 4419, 8347, 25041

Step-4: Factors of 75135

List of positive integer factors of 75135 that divides 75123 without a remainder.

1, 3, 5, 15, 5009, 15027, 25045

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75123 and 75135. The biggest common factor number is the GCF number.
So the greatest common factor 75123 and 75135 is 3.

Also check out the Least Common Multiple of 75123 and 75135