What is the Greatest Common Factor of 75138 and 75145?

Greatest common factor (GCF) of 75138 and 75145 is 7.

GCF(75138,75145) = 7

We will now calculate the prime factors of 75138 and 75145, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75138 and 75145.

How to find the GCF of 75138 and 75145?

We will first find the prime factorization of 75138 and 75145. After we will calculate the factors of 75138 and 75145 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 75145

Prime factors of 75145 are 5, 7, 19, 113. Prime factorization of 75145 in exponential form is:

75145 = 5¹ × 7¹ × 19¹ × 113¹

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 75145

List of positive integer factors of 75145 that divides 75138 without a remainder.

1, 5, 7, 19, 35, 95, 113, 133, 565, 665, 791, 2147, 3955, 10735, 15029

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75138 and 75145. The biggest common factor number is the GCF number.
So the greatest common factor 75138 and 75145 is 7.

Also check out the Least Common Multiple of 75138 and 75145