What is the Greatest Common Factor of 39100 and 39120?

Greatest common factor (GCF) of 39100 and 39120 is 20.

GCF(39100,39120) = 20

We will now calculate the prime factors of 39100 and 39120, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39100 and 39120.

How to find the GCF of 39100 and 39120?

We will first find the prime factorization of 39100 and 39120. After we will calculate the factors of 39100 and 39120 and find the biggest common factor number .

Step-1: Prime Factorization of 39100

Prime factors of 39100 are 2, 5, 17, 23. Prime factorization of 39100 in exponential form is:

39100 = 2² × 5² × 17¹ × 23¹

Step-2: 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-3: Factors of 39100

List of positive integer factors of 39100 that divides 39100 without a remainder.

1, 2, 4, 5, 10, 17, 20, 23, 25, 34, 46, 50, 68, 85, 92, 100, 115, 170, 230, 340, 391, 425, 460, 575, 782, 850, 1150, 1564, 1700, 1955, 2300, 3910, 7820, 9775, 19550

Step-4: Factors of 39120

List of positive integer factors of 39120 that divides 39100 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39100 and 39120. The biggest common factor number is the GCF number.
So the greatest common factor 39100 and 39120 is 20.

Also check out the Least Common Multiple of 39100 and 39120