What is the Greatest Common Factor of 75744 and 75761?

Greatest common factor (GCF) of 75744 and 75761 is 1.

GCF(75744,75761) = 1

We will now calculate the prime factors of 75744 and 75761, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75744 and 75761.

How to find the GCF of 75744 and 75761?

We will first find the prime factorization of 75744 and 75761. After we will calculate the factors of 75744 and 75761 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 75761

Prime factors of 75761 are 7, 79, 137. Prime factorization of 75761 in exponential form is:

75761 = 7¹ × 79¹ × 137¹

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 75761

List of positive integer factors of 75761 that divides 75744 without a remainder.

1, 7, 79, 137, 553, 959, 10823

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75744 and 75761. The biggest common factor number is the GCF number.
So the greatest common factor 75744 and 75761 is 1.

Also check out the Least Common Multiple of 75744 and 75761