What is the Greatest Common Factor of 82124 and 82138?

Greatest common factor (GCF) of 82124 and 82138 is 14.

GCF(82124,82138) = 14

We will now calculate the prime factors of 82124 and 82138, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 82124 and 82138.

How to find the GCF of 82124 and 82138?

We will first find the prime factorization of 82124 and 82138. After we will calculate the factors of 82124 and 82138 and find the biggest common factor number .

Step-1: Prime Factorization of 82124

Prime factors of 82124 are 2, 7, 419. Prime factorization of 82124 in exponential form is:

82124 = 2² × 7² × 419¹

Step-2: Prime Factorization of 82138

Prime factors of 82138 are 2, 7, 5867. Prime factorization of 82138 in exponential form is:

82138 = 2¹ × 7¹ × 5867¹

Step-3: Factors of 82124

List of positive integer factors of 82124 that divides 82124 without a remainder.

1, 2, 4, 7, 14, 28, 49, 98, 196, 419, 838, 1676, 2933, 5866, 11732, 20531, 41062

Step-4: Factors of 82138

List of positive integer factors of 82138 that divides 82124 without a remainder.

1, 2, 7, 14, 5867, 11734, 41069

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 82124 and 82138. The biggest common factor number is the GCF number.
So the greatest common factor 82124 and 82138 is 14.

Also check out the Least Common Multiple of 82124 and 82138