What is the Greatest Common Factor of 75738 and 75744?

Greatest common factor (GCF) of 75738 and 75744 is 6.

GCF(75738,75744) = 6

We will now calculate the prime factors of 75738 and 75744, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75738 and 75744.

How to find the GCF of 75738 and 75744?

We will first find the prime factorization of 75738 and 75744. After we will calculate the factors of 75738 and 75744 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 75744

Prime factors of 75744 are 2, 3, 263. Prime factorization of 75744 in exponential form is:

75744 = 2⁵ × 3² × 263¹

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 75744

List of positive integer factors of 75744 that divides 75738 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 263, 288, 526, 789, 1052, 1578, 2104, 2367, 3156, 4208, 4734, 6312, 8416, 9468, 12624, 18936, 25248, 37872

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75738 and 75744. The biggest common factor number is the GCF number.
So the greatest common factor 75738 and 75744 is 6.

Also check out the Least Common Multiple of 75738 and 75744