What is the Greatest Common Factor of 75810 and 75824?

Greatest common factor (GCF) of 75810 and 75824 is 14.

GCF(75810,75824) = 14

We will now calculate the prime factors of 75810 and 75824, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75810 and 75824.

How to find the GCF of 75810 and 75824?

We will first find the prime factorization of 75810 and 75824. After we will calculate the factors of 75810 and 75824 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 75824

Prime factors of 75824 are 2, 7, 677. Prime factorization of 75824 in exponential form is:

75824 = 2⁴ × 7¹ × 677¹

Step-3: Factors of 75810

List of positive integer factors of 75810 that divides 75810 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

Step-4: Factors of 75824

List of positive integer factors of 75824 that divides 75810 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 56, 112, 677, 1354, 2708, 4739, 5416, 9478, 10832, 18956, 37912

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75810 and 75824. The biggest common factor number is the GCF number.
So the greatest common factor 75810 and 75824 is 14.

Also check out the Least Common Multiple of 75810 and 75824