What is the Greatest Common Factor of 75760 and 75772?

Greatest common factor (GCF) of 75760 and 75772 is 4.

GCF(75760,75772) = 4

We will now calculate the prime factors of 75760 and 75772, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75760 and 75772.

How to find the GCF of 75760 and 75772?

We will first find the prime factorization of 75760 and 75772. After we will calculate the factors of 75760 and 75772 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 75772

Prime factors of 75772 are 2, 19, 997. Prime factorization of 75772 in exponential form is:

75772 = 2² × 19¹ × 997¹

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 75772

List of positive integer factors of 75772 that divides 75760 without a remainder.

1, 2, 4, 19, 38, 76, 997, 1994, 3988, 18943, 37886

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75760 and 75772. The biggest common factor number is the GCF number.
So the greatest common factor 75760 and 75772 is 4.

Also check out the Least Common Multiple of 75760 and 75772