What is the Greatest Common Factor of 82740 and 82754?

Greatest common factor (GCF) of 82740 and 82754 is 14.

GCF(82740,82754) = 14

We will now calculate the prime factors of 82740 and 82754, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 82740 and 82754.

How to find the GCF of 82740 and 82754?

We will first find the prime factorization of 82740 and 82754. After we will calculate the factors of 82740 and 82754 and find the biggest common factor number .

Step-1: Prime Factorization of 82740

Prime factors of 82740 are 2, 3, 5, 7, 197. Prime factorization of 82740 in exponential form is:

82740 = 2² × 3¹ × 5¹ × 7¹ × 197¹

Step-2: Prime Factorization of 82754

Prime factors of 82754 are 2, 7, 23, 257. Prime factorization of 82754 in exponential form is:

82754 = 2¹ × 7¹ × 23¹ × 257¹

Step-3: Factors of 82740

List of positive integer factors of 82740 that divides 82740 without a remainder.

1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 197, 210, 394, 420, 591, 788, 985, 1182, 1379, 1970, 2364, 2758, 2955, 3940, 4137, 5516, 5910, 6895, 8274, 11820, 13790, 16548, 20685, 27580, 41370

Step-4: Factors of 82754

List of positive integer factors of 82754 that divides 82740 without a remainder.

1, 2, 7, 14, 23, 46, 161, 257, 322, 514, 1799, 3598, 5911, 11822, 41377

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 82740 and 82754. The biggest common factor number is the GCF number.
So the greatest common factor 82740 and 82754 is 14.

Also check out the Least Common Multiple of 82740 and 82754