What is the Greatest Common Factor of 75888 and 75900?

Greatest common factor (GCF) of 75888 and 75900 is 12.

GCF(75888,75900) = 12

We will now calculate the prime factors of 75888 and 75900, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75888 and 75900.

How to find the GCF of 75888 and 75900?

We will first find the prime factorization of 75888 and 75900. After we will calculate the factors of 75888 and 75900 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 75900

Prime factors of 75900 are 2, 3, 5, 11, 23. Prime factorization of 75900 in exponential form is:

75900 = 2² × 3¹ × 5² × 11¹ × 23¹

Step-3: Factors of 75888

List of positive integer factors of 75888 that divides 75888 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

Step-4: Factors of 75900

List of positive integer factors of 75900 that divides 75888 without a remainder.

1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 23, 25, 30, 33, 44, 46, 50, 55, 60, 66, 69, 75, 92, 100, 110, 115, 132, 138, 150, 165, 220, 230, 253, 275, 276, 300, 330, 345, 460, 506, 550, 575, 660, 690, 759, 825, 1012, 1100, 1150, 1265, 1380, 1518, 1650, 1725, 2300, 2530, 3036, 3300, 3450, 3795, 5060, 6325, 6900, 7590, 12650, 15180, 18975, 25300, 37950

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75888 and 75900. The biggest common factor number is the GCF number.
So the greatest common factor 75888 and 75900 is 12.

Also check out the Least Common Multiple of 75888 and 75900