What is the Greatest Common Factor of 75768 and 75782?

Greatest common factor (GCF) of 75768 and 75782 is 14.

GCF(75768,75782) = 14

We will now calculate the prime factors of 75768 and 75782, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75768 and 75782.

How to find the GCF of 75768 and 75782?

We will first find the prime factorization of 75768 and 75782. After we will calculate the factors of 75768 and 75782 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 75782

Prime factors of 75782 are 2, 7, 5413. Prime factorization of 75782 in exponential form is:

75782 = 2¹ × 7¹ × 5413¹

Step-3: Factors of 75768

List of positive integer factors of 75768 that divides 75768 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

Step-4: Factors of 75782

List of positive integer factors of 75782 that divides 75768 without a remainder.

1, 2, 7, 14, 5413, 10826, 37891

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75768 and 75782. The biggest common factor number is the GCF number.
So the greatest common factor 75768 and 75782 is 14.

Also check out the Least Common Multiple of 75768 and 75782