What is the Greatest Common Factor of 75814 and 75828?

Greatest common factor (GCF) of 75814 and 75828 is 2.

GCF(75814,75828) = 2

We will now calculate the prime factors of 75814 and 75828, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75814 and 75828.

How to find the GCF of 75814 and 75828?

We will first find the prime factorization of 75814 and 75828. After we will calculate the factors of 75814 and 75828 and find the biggest common factor number .

Step-1: Prime Factorization of 75814

Prime factors of 75814 are 2, 37907. Prime factorization of 75814 in exponential form is:

75814 = 2¹ × 37907¹

Step-2: Prime Factorization of 75828

Prime factors of 75828 are 2, 3, 71, 89. Prime factorization of 75828 in exponential form is:

75828 = 2² × 3¹ × 71¹ × 89¹

Step-3: Factors of 75814

List of positive integer factors of 75814 that divides 75814 without a remainder.

1, 2, 37907

Step-4: Factors of 75828

List of positive integer factors of 75828 that divides 75814 without a remainder.

1, 2, 3, 4, 6, 12, 71, 89, 142, 178, 213, 267, 284, 356, 426, 534, 852, 1068, 6319, 12638, 18957, 25276, 37914

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75814 and 75828. The biggest common factor number is the GCF number.
So the greatest common factor 75814 and 75828 is 2.

Also check out the Least Common Multiple of 75814 and 75828