What is the Greatest Common Factor of 75138 and 75153?

Greatest common factor (GCF) of 75138 and 75153 is 3.

GCF(75138,75153) = 3

We will now calculate the prime factors of 75138 and 75153, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75138 and 75153.

How to find the GCF of 75138 and 75153?

We will first find the prime factorization of 75138 and 75153. After we will calculate the factors of 75138 and 75153 and find the biggest common factor number .

Step-1: Prime Factorization of 75138

Prime factors of 75138 are 2, 3, 7, 1789. Prime factorization of 75138 in exponential form is:

75138 = 2¹ × 3¹ × 7¹ × 1789¹

Step-2: Prime Factorization of 75153

Prime factors of 75153 are 3, 13, 41, 47. Prime factorization of 75153 in exponential form is:

75153 = 3¹ × 13¹ × 41¹ × 47¹

Step-3: Factors of 75138

List of positive integer factors of 75138 that divides 75138 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 1789, 3578, 5367, 10734, 12523, 25046, 37569

Step-4: Factors of 75153

List of positive integer factors of 75153 that divides 75138 without a remainder.

1, 3, 13, 39, 41, 47, 123, 141, 533, 611, 1599, 1833, 1927, 5781, 25051

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75138 and 75153. The biggest common factor number is the GCF number.
So the greatest common factor 75138 and 75153 is 3.

Also check out the Least Common Multiple of 75138 and 75153