What is the Greatest Common Factor of 75760 and 75774?

Greatest common factor (GCF) of 75760 and 75774 is 2.

GCF(75760,75774) = 2

We will now calculate the prime factors of 75760 and 75774, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75760 and 75774.

How to find the GCF of 75760 and 75774?

We will first find the prime factorization of 75760 and 75774. After we will calculate the factors of 75760 and 75774 and find the biggest common factor number .

Step-1: Prime Factorization of 75760

Prime factors of 75760 are 2, 5, 947. Prime factorization of 75760 in exponential form is:

75760 = 2⁴ × 5¹ × 947¹

Step-2: Prime Factorization of 75774

Prime factors of 75774 are 2, 3, 73, 173. Prime factorization of 75774 in exponential form is:

75774 = 2¹ × 3¹ × 73¹ × 173¹

Step-3: Factors of 75760

List of positive integer factors of 75760 that divides 75760 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 40, 80, 947, 1894, 3788, 4735, 7576, 9470, 15152, 18940, 37880

Step-4: Factors of 75774

List of positive integer factors of 75774 that divides 75760 without a remainder.

1, 2, 3, 6, 73, 146, 173, 219, 346, 438, 519, 1038, 12629, 25258, 37887

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75760 and 75774. The biggest common factor number is the GCF number.
So the greatest common factor 75760 and 75774 is 2.

Also check out the Least Common Multiple of 75760 and 75774