What is the Greatest Common Factor of 75824 and 75830?

Greatest common factor (GCF) of 75824 and 75830 is 2.

GCF(75824,75830) = 2

We will now calculate the prime factors of 75824 and 75830, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75824 and 75830.

How to find the GCF of 75824 and 75830?

We will first find the prime factorization of 75824 and 75830. After we will calculate the factors of 75824 and 75830 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 75830

Prime factors of 75830 are 2, 5, 7583. Prime factorization of 75830 in exponential form is:

75830 = 2¹ × 5¹ × 7583¹

Step-3: Factors of 75824

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

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

Step-4: Factors of 75830

List of positive integer factors of 75830 that divides 75824 without a remainder.

1, 2, 5, 10, 7583, 15166, 37915

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75824 and 75830. The biggest common factor number is the GCF number.
So the greatest common factor 75824 and 75830 is 2.

Also check out the Least Common Multiple of 75824 and 75830