What is the Greatest Common Factor of 75760 and 75780?

Greatest common factor (GCF) of 75760 and 75780 is 20.

GCF(75760,75780) = 20

We will now calculate the prime factors of 75760 and 75780, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75760 and 75780.

How to find the GCF of 75760 and 75780?

We will first find the prime factorization of 75760 and 75780. After we will calculate the factors of 75760 and 75780 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 75780

Prime factors of 75780 are 2, 3, 5, 421. Prime factorization of 75780 in exponential form is:

75780 = 2² × 3² × 5¹ × 421¹

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 75780

List of positive integer factors of 75780 that divides 75760 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180, 421, 842, 1263, 1684, 2105, 2526, 3789, 4210, 5052, 6315, 7578, 8420, 12630, 15156, 18945, 25260, 37890

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75760 and 75780. The biggest common factor number is the GCF number.
So the greatest common factor 75760 and 75780 is 20.

Also check out the Least Common Multiple of 75760 and 75780