What is the Greatest Common Factor of 75753 and 75768?

Greatest common factor (GCF) of 75753 and 75768 is 3.

GCF(75753,75768) = 3

We will now calculate the prime factors of 75753 and 75768, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75753 and 75768.

How to find the GCF of 75753 and 75768?

We will first find the prime factorization of 75753 and 75768. After we will calculate the factors of 75753 and 75768 and find the biggest common factor number .

Step-1: Prime Factorization of 75753

Prime factors of 75753 are 3, 19, 443. Prime factorization of 75753 in exponential form is:

75753 = 3² × 19¹ × 443¹

Step-2: Prime Factorization of 75768

Prime factors of 75768 are 2, 3, 7, 11, 41. Prime factorization of 75768 in exponential form is:

75768 = 2³ × 3¹ × 7¹ × 11¹ × 41¹

Step-3: Factors of 75753

List of positive integer factors of 75753 that divides 75753 without a remainder.

1, 3, 9, 19, 57, 171, 443, 1329, 3987, 8417, 25251

Step-4: Factors of 75768

List of positive integer factors of 75768 that divides 75753 without a remainder.

1, 2, 3, 4, 6, 7, 8, 11, 12, 14, 21, 22, 24, 28, 33, 41, 42, 44, 56, 66, 77, 82, 84, 88, 123, 132, 154, 164, 168, 231, 246, 264, 287, 308, 328, 451, 462, 492, 574, 616, 861, 902, 924, 984, 1148, 1353, 1722, 1804, 1848, 2296, 2706, 3157, 3444, 3608, 5412, 6314, 6888, 9471, 10824, 12628, 18942, 25256, 37884

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75753 and 75768. The biggest common factor number is the GCF number.
So the greatest common factor 75753 and 75768 is 3.

Also check out the Least Common Multiple of 75753 and 75768