What is the Greatest Common Factor of 75828 and 75842?

Greatest common factor (GCF) of 75828 and 75842 is 2.

GCF(75828,75842) = 2

We will now calculate the prime factors of 75828 and 75842, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75828 and 75842.

How to find the GCF of 75828 and 75842?

We will first find the prime factorization of 75828 and 75842. After we will calculate the factors of 75828 and 75842 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 75842

Prime factors of 75842 are 2, 13, 2917. Prime factorization of 75842 in exponential form is:

75842 = 2¹ × 13¹ × 2917¹

Step-3: Factors of 75828

List of positive integer factors of 75828 that divides 75828 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

Step-4: Factors of 75842

List of positive integer factors of 75842 that divides 75828 without a remainder.

1, 2, 13, 26, 2917, 5834, 37921

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75828 and 75842. The biggest common factor number is the GCF number.
So the greatest common factor 75828 and 75842 is 2.

Also check out the Least Common Multiple of 75828 and 75842