What is the Greatest Common Factor of 39120 and 39140?

Greatest common factor (GCF) of 39120 and 39140 is 20.

GCF(39120,39140) = 20

We will now calculate the prime factors of 39120 and 39140, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39120 and 39140.

How to find the GCF of 39120 and 39140?

We will first find the prime factorization of 39120 and 39140. After we will calculate the factors of 39120 and 39140 and find the biggest common factor number .

Step-1: Prime Factorization of 39120

Prime factors of 39120 are 2, 3, 5, 163. Prime factorization of 39120 in exponential form is:

39120 = 2⁴ × 3¹ × 5¹ × 163¹

Step-2: Prime Factorization of 39140

Prime factors of 39140 are 2, 5, 19, 103. Prime factorization of 39140 in exponential form is:

39140 = 2² × 5¹ × 19¹ × 103¹

Step-3: Factors of 39120

List of positive integer factors of 39120 that divides 39120 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 163, 240, 326, 489, 652, 815, 978, 1304, 1630, 1956, 2445, 2608, 3260, 3912, 4890, 6520, 7824, 9780, 13040, 19560

Step-4: Factors of 39140

List of positive integer factors of 39140 that divides 39120 without a remainder.

1, 2, 4, 5, 10, 19, 20, 38, 76, 95, 103, 190, 206, 380, 412, 515, 1030, 1957, 2060, 3914, 7828, 9785, 19570

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39120 and 39140. The biggest common factor number is the GCF number.
So the greatest common factor 39120 and 39140 is 20.

Also check out the Least Common Multiple of 39120 and 39140