What is the Greatest Common Factor of 75738 and 75756?

Greatest common factor (GCF) of 75738 and 75756 is 6.

GCF(75738,75756) = 6

We will now calculate the prime factors of 75738 and 75756, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75738 and 75756.

How to find the GCF of 75738 and 75756?

We will first find the prime factorization of 75738 and 75756. After we will calculate the factors of 75738 and 75756 and find the biggest common factor number .

Step-1: Prime Factorization of 75738

Prime factors of 75738 are 2, 3, 13, 971. Prime factorization of 75738 in exponential form is:

75738 = 2¹ × 3¹ × 13¹ × 971¹

Step-2: Prime Factorization of 75756

Prime factors of 75756 are 2, 3, 59, 107. Prime factorization of 75756 in exponential form is:

75756 = 2² × 3¹ × 59¹ × 107¹

Step-3: Factors of 75738

List of positive integer factors of 75738 that divides 75738 without a remainder.

1, 2, 3, 6, 13, 26, 39, 78, 971, 1942, 2913, 5826, 12623, 25246, 37869

Step-4: Factors of 75756

List of positive integer factors of 75756 that divides 75738 without a remainder.

1, 2, 3, 4, 6, 12, 59, 107, 118, 177, 214, 236, 321, 354, 428, 642, 708, 1284, 6313, 12626, 18939, 25252, 37878

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75738 and 75756. The biggest common factor number is the GCF number.
So the greatest common factor 75738 and 75756 is 6.

Also check out the Least Common Multiple of 75738 and 75756