What is the Greatest Common Factor of 81998 and 82012?

Greatest common factor (GCF) of 81998 and 82012 is 14.

GCF(81998,82012) = 14

We will now calculate the prime factors of 81998 and 82012, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 81998 and 82012.

How to find the GCF of 81998 and 82012?

We will first find the prime factorization of 81998 and 82012. After we will calculate the factors of 81998 and 82012 and find the biggest common factor number .

Step-1: Prime Factorization of 81998

Prime factors of 81998 are 2, 7, 5857. Prime factorization of 81998 in exponential form is:

81998 = 2¹ × 7¹ × 5857¹

Step-2: Prime Factorization of 82012

Prime factors of 82012 are 2, 7, 29, 101. Prime factorization of 82012 in exponential form is:

82012 = 2² × 7¹ × 29¹ × 101¹

Step-3: Factors of 81998

List of positive integer factors of 81998 that divides 81998 without a remainder.

1, 2, 7, 14, 5857, 11714, 40999

Step-4: Factors of 82012

List of positive integer factors of 82012 that divides 81998 without a remainder.

1, 2, 4, 7, 14, 28, 29, 58, 101, 116, 202, 203, 404, 406, 707, 812, 1414, 2828, 2929, 5858, 11716, 20503, 41006

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 81998 and 82012. The biggest common factor number is the GCF number.
So the greatest common factor 81998 and 82012 is 14.

Also check out the Least Common Multiple of 81998 and 82012