What is the Greatest Common Factor of 20140 and 20150?

Greatest common factor (GCF) of 20140 and 20150 is 10.

GCF(20140,20150) = 10

We will now calculate the prime factors of 20140 and 20150, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 20140 and 20150.

How to find the GCF of 20140 and 20150?

We will first find the prime factorization of 20140 and 20150. After we will calculate the factors of 20140 and 20150 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 20150

Prime factors of 20150 are 2, 5, 13, 31. Prime factorization of 20150 in exponential form is:

20150 = 2¹ × 5² × 13¹ × 31¹

Step-3: Factors of 20140

List of positive integer factors of 20140 that divides 20140 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

Step-4: Factors of 20150

List of positive integer factors of 20150 that divides 20140 without a remainder.

1, 2, 5, 10, 13, 25, 26, 31, 50, 62, 65, 130, 155, 310, 325, 403, 650, 775, 806, 1550, 2015, 4030, 10075

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 20140 and 20150. The biggest common factor number is the GCF number.
So the greatest common factor 20140 and 20150 is 10.

Also check out the Least Common Multiple of 20140 and 20150