What is the Greatest Common Factor of 75792 and 75810?

Greatest common factor (GCF) of 75792 and 75810 is 6.

GCF(75792,75810) = 6

We will now calculate the prime factors of 75792 and 75810, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75792 and 75810.

How to find the GCF of 75792 and 75810?

We will first find the prime factorization of 75792 and 75810. After we will calculate the factors of 75792 and 75810 and find the biggest common factor number .

Step-1: Prime Factorization of 75792

Prime factors of 75792 are 2, 3, 1579. Prime factorization of 75792 in exponential form is:

75792 = 2⁴ × 3¹ × 1579¹

Step-2: Prime Factorization of 75810

Prime factors of 75810 are 2, 3, 5, 7, 19. Prime factorization of 75810 in exponential form is:

75810 = 2¹ × 3¹ × 5¹ × 7¹ × 19²

Step-3: Factors of 75792

List of positive integer factors of 75792 that divides 75792 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 1579, 3158, 4737, 6316, 9474, 12632, 18948, 25264, 37896

Step-4: Factors of 75810

List of positive integer factors of 75810 that divides 75792 without a remainder.

1, 2, 3, 5, 6, 7, 10, 14, 15, 19, 21, 30, 35, 38, 42, 57, 70, 95, 105, 114, 133, 190, 210, 266, 285, 361, 399, 570, 665, 722, 798, 1083, 1330, 1805, 1995, 2166, 2527, 3610, 3990, 5054, 5415, 7581, 10830, 12635, 15162, 25270, 37905

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75792 and 75810. The biggest common factor number is the GCF number.
So the greatest common factor 75792 and 75810 is 6.

Also check out the Least Common Multiple of 75792 and 75810