What is the Greatest Common Factor of 83700 and 83720?

Greatest common factor (GCF) of 83700 and 83720 is 20.

GCF(83700,83720) = 20

We will now calculate the prime factors of 83700 and 83720, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 83700 and 83720.

How to find the GCF of 83700 and 83720?

We will first find the prime factorization of 83700 and 83720. After we will calculate the factors of 83700 and 83720 and find the biggest common factor number .

Step-1: Prime Factorization of 83700

Prime factors of 83700 are 2, 3, 5, 31. Prime factorization of 83700 in exponential form is:

83700 = 2² × 3³ × 5² × 31¹

Step-2: Prime Factorization of 83720

Prime factors of 83720 are 2, 5, 7, 13, 23. Prime factorization of 83720 in exponential form is:

83720 = 2³ × 5¹ × 7¹ × 13¹ × 23¹

Step-3: Factors of 83700

List of positive integer factors of 83700 that divides 83700 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 27, 30, 31, 36, 45, 50, 54, 60, 62, 75, 90, 93, 100, 108, 124, 135, 150, 155, 180, 186, 225, 270, 279, 300, 310, 372, 450, 465, 540, 558, 620, 675, 775, 837, 900, 930, 1116, 1350, 1395, 1550, 1674, 1860, 2325, 2700, 2790, 3100, 3348, 4185, 4650, 5580, 6975, 8370, 9300, 13950, 16740, 20925, 27900, 41850

Step-4: Factors of 83720

List of positive integer factors of 83720 that divides 83700 without a remainder.

1, 2, 4, 5, 7, 8, 10, 13, 14, 20, 23, 26, 28, 35, 40, 46, 52, 56, 65, 70, 91, 92, 104, 115, 130, 140, 161, 182, 184, 230, 260, 280, 299, 322, 364, 455, 460, 520, 598, 644, 728, 805, 910, 920, 1196, 1288, 1495, 1610, 1820, 2093, 2392, 2990, 3220, 3640, 4186, 5980, 6440, 8372, 10465, 11960, 16744, 20930, 41860

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 83700 and 83720. The biggest common factor number is the GCF number.
So the greatest common factor 83700 and 83720 is 20.

Also check out the Least Common Multiple of 83700 and 83720