What is the Greatest Common Factor of 20128 and 20140?

Greatest common factor (GCF) of 20128 and 20140 is 4.

GCF(20128,20140) = 4

We will now calculate the prime factors of 20128 and 20140, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 20128 and 20140.

How to find the GCF of 20128 and 20140?

We will first find the prime factorization of 20128 and 20140. After we will calculate the factors of 20128 and 20140 and find the biggest common factor number .

Step-1: Prime Factorization of 20128

Prime factors of 20128 are 2, 17, 37. Prime factorization of 20128 in exponential form is:

20128 = 2⁵ × 17¹ × 37¹

Step-2: Prime Factorization of 20140

Prime factors of 20140 are 2, 5, 19, 53. Prime factorization of 20140 in exponential form is:

20140 = 2² × 5¹ × 19¹ × 53¹

Step-3: Factors of 20128

List of positive integer factors of 20128 that divides 20128 without a remainder.

1, 2, 4, 8, 16, 17, 32, 34, 37, 68, 74, 136, 148, 272, 296, 544, 592, 629, 1184, 1258, 2516, 5032, 10064

Step-4: Factors of 20140

List of positive integer factors of 20140 that divides 20128 without a remainder.

1, 2, 4, 5, 10, 19, 20, 38, 53, 76, 95, 106, 190, 212, 265, 380, 530, 1007, 1060, 2014, 4028, 5035, 10070

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 20128 and 20140. The biggest common factor number is the GCF number.
So the greatest common factor 20128 and 20140 is 4.

Also check out the Least Common Multiple of 20128 and 20140