What is the Greatest Common Factor of 20120 and 20130?

Greatest common factor (GCF) of 20120 and 20130 is 10.

GCF(20120,20130) = 10

We will now calculate the prime factors of 20120 and 20130, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 20120 and 20130.

How to find the GCF of 20120 and 20130?

We will first find the prime factorization of 20120 and 20130. After we will calculate the factors of 20120 and 20130 and find the biggest common factor number .

Step-1: Prime Factorization of 20120

Prime factors of 20120 are 2, 5, 503. Prime factorization of 20120 in exponential form is:

20120 = 2³ × 5¹ × 503¹

Step-2: Prime Factorization of 20130

Prime factors of 20130 are 2, 3, 5, 11, 61. Prime factorization of 20130 in exponential form is:

20130 = 2¹ × 3¹ × 5¹ × 11¹ × 61¹

Step-3: Factors of 20120

List of positive integer factors of 20120 that divides 20120 without a remainder.

1, 2, 4, 5, 8, 10, 20, 40, 503, 1006, 2012, 2515, 4024, 5030, 10060

Step-4: Factors of 20130

List of positive integer factors of 20130 that divides 20120 without a remainder.

1, 2, 3, 5, 6, 10, 11, 15, 22, 30, 33, 55, 61, 66, 110, 122, 165, 183, 305, 330, 366, 610, 671, 915, 1342, 1830, 2013, 3355, 4026, 6710, 10065

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 20120 and 20130. The biggest common factor number is the GCF number.
So the greatest common factor 20120 and 20130 is 10.

Also check out the Least Common Multiple of 20120 and 20130