What is the Greatest Common Factor of 75744 and 75764?

Greatest common factor (GCF) of 75744 and 75764 is 4.

GCF(75744,75764) = 4

We will now calculate the prime factors of 75744 and 75764, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75744 and 75764.

How to find the GCF of 75744 and 75764?

We will first find the prime factorization of 75744 and 75764. After we will calculate the factors of 75744 and 75764 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 75764

Prime factors of 75764 are 2, 13, 31, 47. Prime factorization of 75764 in exponential form is:

75764 = 2² × 13¹ × 31¹ × 47¹

Step-3: Factors of 75744

List of positive integer factors of 75744 that divides 75744 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

Step-4: Factors of 75764

List of positive integer factors of 75764 that divides 75744 without a remainder.

1, 2, 4, 13, 26, 31, 47, 52, 62, 94, 124, 188, 403, 611, 806, 1222, 1457, 1612, 2444, 2914, 5828, 18941, 37882

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75744 and 75764. The biggest common factor number is the GCF number.
So the greatest common factor 75744 and 75764 is 4.

Also check out the Least Common Multiple of 75744 and 75764