What is the Greatest Common Factor of 75872 and 75888?

Greatest common factor (GCF) of 75872 and 75888 is 16.

GCF(75872,75888) = 16

We will now calculate the prime factors of 75872 and 75888, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75872 and 75888.

How to find the GCF of 75872 and 75888?

We will first find the prime factorization of 75872 and 75888. After we will calculate the factors of 75872 and 75888 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 75888

Prime factors of 75888 are 2, 3, 17, 31. Prime factorization of 75888 in exponential form is:

75888 = 2⁴ × 3² × 17¹ × 31¹

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 75888

List of positive integer factors of 75888 that divides 75872 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 17, 18, 24, 31, 34, 36, 48, 51, 62, 68, 72, 93, 102, 124, 136, 144, 153, 186, 204, 248, 272, 279, 306, 372, 408, 496, 527, 558, 612, 744, 816, 1054, 1116, 1224, 1488, 1581, 2108, 2232, 2448, 3162, 4216, 4464, 4743, 6324, 8432, 9486, 12648, 18972, 25296, 37944

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75872 and 75888. The biggest common factor number is the GCF number.
So the greatest common factor 75872 and 75888 is 16.

Also check out the Least Common Multiple of 75872 and 75888