What is the Greatest Common Factor of 75872 and 75880?

Greatest common factor (GCF) of 75872 and 75880 is 8.

GCF(75872,75880) = 8

We will now calculate the prime factors of 75872 and 75880, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75872 and 75880.

How to find the GCF of 75872 and 75880?

We will first find the prime factorization of 75872 and 75880. After we will calculate the factors of 75872 and 75880 and find the biggest common factor number .

Step-1: Prime Factorization of 75872

Prime factors of 75872 are 2, 2371. Prime factorization of 75872 in exponential form is:

75872 = 2⁵ × 2371¹

Step-2: Prime Factorization of 75880

Prime factors of 75880 are 2, 5, 7, 271. Prime factorization of 75880 in exponential form is:

75880 = 2³ × 5¹ × 7¹ × 271¹

Step-3: Factors of 75872

List of positive integer factors of 75872 that divides 75872 without a remainder.

1, 2, 4, 8, 16, 32, 2371, 4742, 9484, 18968, 37936

Step-4: Factors of 75880

List of positive integer factors of 75880 that divides 75872 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 140, 271, 280, 542, 1084, 1355, 1897, 2168, 2710, 3794, 5420, 7588, 9485, 10840, 15176, 18970, 37940

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75872 and 75880. The biggest common factor number is the GCF number.
So the greatest common factor 75872 and 75880 is 8.

Also check out the Least Common Multiple of 75872 and 75880