What is the Greatest Common Factor of 82414 and 82420?

Greatest common factor (GCF) of 82414 and 82420 is 2.

GCF(82414,82420) = 2

We will now calculate the prime factors of 82414 and 82420, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 82414 and 82420.

How to find the GCF of 82414 and 82420?

We will first find the prime factorization of 82414 and 82420. After we will calculate the factors of 82414 and 82420 and find the biggest common factor number .

Step-1: Prime Factorization of 82414

Prime factors of 82414 are 2, 89, 463. Prime factorization of 82414 in exponential form is:

82414 = 2¹ × 89¹ × 463¹

Step-2: Prime Factorization of 82420

Prime factors of 82420 are 2, 5, 13, 317. Prime factorization of 82420 in exponential form is:

82420 = 2² × 5¹ × 13¹ × 317¹

Step-3: Factors of 82414

List of positive integer factors of 82414 that divides 82414 without a remainder.

1, 2, 89, 178, 463, 926, 41207

Step-4: Factors of 82420

List of positive integer factors of 82420 that divides 82414 without a remainder.

1, 2, 4, 5, 10, 13, 20, 26, 52, 65, 130, 260, 317, 634, 1268, 1585, 3170, 4121, 6340, 8242, 16484, 20605, 41210

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 82414 and 82420. The biggest common factor number is the GCF number.
So the greatest common factor 82414 and 82420 is 2.

Also check out the Least Common Multiple of 82414 and 82420