What is the Greatest Common Factor of 75396 and 75414?

Greatest common factor (GCF) of 75396 and 75414 is 6.

GCF(75396,75414) = 6

We will now calculate the prime factors of 75396 and 75414, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75396 and 75414.

How to find the GCF of 75396 and 75414?

We will first find the prime factorization of 75396 and 75414. After we will calculate the factors of 75396 and 75414 and find the biggest common factor number .

Step-1: Prime Factorization of 75396

Prime factors of 75396 are 2, 3, 61, 103. Prime factorization of 75396 in exponential form is:

75396 = 2² × 3¹ × 61¹ × 103¹

Step-2: Prime Factorization of 75414

Prime factors of 75414 are 2, 3, 12569. Prime factorization of 75414 in exponential form is:

75414 = 2¹ × 3¹ × 12569¹

Step-3: Factors of 75396

List of positive integer factors of 75396 that divides 75396 without a remainder.

1, 2, 3, 4, 6, 12, 61, 103, 122, 183, 206, 244, 309, 366, 412, 618, 732, 1236, 6283, 12566, 18849, 25132, 37698

Step-4: Factors of 75414

List of positive integer factors of 75414 that divides 75396 without a remainder.

1, 2, 3, 6, 12569, 25138, 37707

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75396 and 75414. The biggest common factor number is the GCF number.
So the greatest common factor 75396 and 75414 is 6.

Also check out the Least Common Multiple of 75396 and 75414