What is the Greatest Common Factor of 82138 and 82144?

Greatest common factor (GCF) of 82138 and 82144 is 2.

GCF(82138,82144) = 2

We will now calculate the prime factors of 82138 and 82144, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 82138 and 82144.

How to find the GCF of 82138 and 82144?

We will first find the prime factorization of 82138 and 82144. After we will calculate the factors of 82138 and 82144 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 82144

Prime factors of 82144 are 2, 17, 151. Prime factorization of 82144 in exponential form is:

82144 = 2⁵ × 17¹ × 151¹

Step-3: Factors of 82138

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

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

Step-4: Factors of 82144

List of positive integer factors of 82144 that divides 82138 without a remainder.

1, 2, 4, 8, 16, 17, 32, 34, 68, 136, 151, 272, 302, 544, 604, 1208, 2416, 2567, 4832, 5134, 10268, 20536, 41072

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 82138 and 82144. The biggest common factor number is the GCF number.
So the greatest common factor 82138 and 82144 is 2.

Also check out the Least Common Multiple of 82138 and 82144