What is the Greatest Common Factor of 83580 and 83600?

Greatest common factor (GCF) of 83580 and 83600 is 20.

GCF(83580,83600) = 20

We will now calculate the prime factors of 83580 and 83600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 83580 and 83600.

How to find the GCF of 83580 and 83600?

We will first find the prime factorization of 83580 and 83600. After we will calculate the factors of 83580 and 83600 and find the biggest common factor number .

Step-1: Prime Factorization of 83580

Prime factors of 83580 are 2, 3, 5, 7, 199. Prime factorization of 83580 in exponential form is:

83580 = 2² × 3¹ × 5¹ × 7¹ × 199¹

Step-2: Prime Factorization of 83600

Prime factors of 83600 are 2, 5, 11, 19. Prime factorization of 83600 in exponential form is:

83600 = 2⁴ × 5² × 11¹ × 19¹

Step-3: Factors of 83580

List of positive integer factors of 83580 that divides 83580 without a remainder.

1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 199, 210, 398, 420, 597, 796, 995, 1194, 1393, 1990, 2388, 2786, 2985, 3980, 4179, 5572, 5970, 6965, 8358, 11940, 13930, 16716, 20895, 27860, 41790

Step-4: Factors of 83600

List of positive integer factors of 83600 that divides 83580 without a remainder.

1, 2, 4, 5, 8, 10, 11, 16, 19, 20, 22, 25, 38, 40, 44, 50, 55, 76, 80, 88, 95, 100, 110, 152, 176, 190, 200, 209, 220, 275, 304, 380, 400, 418, 440, 475, 550, 760, 836, 880, 950, 1045, 1100, 1520, 1672, 1900, 2090, 2200, 3344, 3800, 4180, 4400, 5225, 7600, 8360, 10450, 16720, 20900, 41800

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 83580 and 83600. The biggest common factor number is the GCF number.
So the greatest common factor 83580 and 83600 is 20.

Also check out the Least Common Multiple of 83580 and 83600