What is the Greatest Common Factor of 39780 and 39800?

Greatest common factor (GCF) of 39780 and 39800 is 20.

GCF(39780,39800) = 20

We will now calculate the prime factors of 39780 and 39800, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39780 and 39800.

How to find the GCF of 39780 and 39800?

We will first find the prime factorization of 39780 and 39800. After we will calculate the factors of 39780 and 39800 and find the biggest common factor number .

Step-1: Prime Factorization of 39780

Prime factors of 39780 are 2, 3, 5, 13, 17. Prime factorization of 39780 in exponential form is:

39780 = 2² × 3² × 5¹ × 13¹ × 17¹

Step-2: Prime Factorization of 39800

Prime factors of 39800 are 2, 5, 199. Prime factorization of 39800 in exponential form is:

39800 = 2³ × 5² × 199¹

Step-3: Factors of 39780

List of positive integer factors of 39780 that divides 39780 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 13, 15, 17, 18, 20, 26, 30, 34, 36, 39, 45, 51, 52, 60, 65, 68, 78, 85, 90, 102, 117, 130, 153, 156, 170, 180, 195, 204, 221, 234, 255, 260, 306, 340, 390, 442, 468, 510, 585, 612, 663, 765, 780, 884, 1020, 1105, 1170, 1326, 1530, 1989, 2210, 2340, 2652, 3060, 3315, 3978, 4420, 6630, 7956, 9945, 13260, 19890

Step-4: Factors of 39800

List of positive integer factors of 39800 that divides 39780 without a remainder.

1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 199, 200, 398, 796, 995, 1592, 1990, 3980, 4975, 7960, 9950, 19900

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39780 and 39800. The biggest common factor number is the GCF number.
So the greatest common factor 39780 and 39800 is 20.

Also check out the Least Common Multiple of 39780 and 39800