What is the Greatest Common Factor of 75138 and 75152?

Greatest common factor (GCF) of 75138 and 75152 is 14.

GCF(75138,75152) = 14

We will now calculate the prime factors of 75138 and 75152, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75138 and 75152.

How to find the GCF of 75138 and 75152?

We will first find the prime factorization of 75138 and 75152. After we will calculate the factors of 75138 and 75152 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 75152

Prime factors of 75152 are 2, 7, 11, 61. Prime factorization of 75152 in exponential form is:

75152 = 2⁴ × 7¹ × 11¹ × 61¹

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 75152

List of positive integer factors of 75152 that divides 75138 without a remainder.

1, 2, 4, 7, 8, 11, 14, 16, 22, 28, 44, 56, 61, 77, 88, 112, 122, 154, 176, 244, 308, 427, 488, 616, 671, 854, 976, 1232, 1342, 1708, 2684, 3416, 4697, 5368, 6832, 9394, 10736, 18788, 37576

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75138 and 75152. The biggest common factor number is the GCF number.
So the greatest common factor 75138 and 75152 is 14.

Also check out the Least Common Multiple of 75138 and 75152