What is the Greatest Common Factor of 75824 and 75838?

Greatest common factor (GCF) of 75824 and 75838 is 14.

GCF(75824,75838) = 14

We will now calculate the prime factors of 75824 and 75838, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75824 and 75838.

How to find the GCF of 75824 and 75838?

We will first find the prime factorization of 75824 and 75838. After we will calculate the factors of 75824 and 75838 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 75838

Prime factors of 75838 are 2, 7, 5417. Prime factorization of 75838 in exponential form is:

75838 = 2¹ × 7¹ × 5417¹

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 75838

List of positive integer factors of 75838 that divides 75824 without a remainder.

1, 2, 7, 14, 5417, 10834, 37919

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75824 and 75838. The biggest common factor number is the GCF number.
So the greatest common factor 75824 and 75838 is 14.

Also check out the Least Common Multiple of 75824 and 75838