What is the Greatest Common Factor of 83500 and 83520?

Greatest common factor (GCF) of 83500 and 83520 is 20.

GCF(83500,83520) = 20

We will now calculate the prime factors of 83500 and 83520, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 83500 and 83520.

How to find the GCF of 83500 and 83520?

We will first find the prime factorization of 83500 and 83520. After we will calculate the factors of 83500 and 83520 and find the biggest common factor number .

Step-1: Prime Factorization of 83500

Prime factors of 83500 are 2, 5, 167. Prime factorization of 83500 in exponential form is:

83500 = 2² × 5³ × 167¹

Step-2: Prime Factorization of 83520

Prime factors of 83520 are 2, 3, 5, 29. Prime factorization of 83520 in exponential form is:

83520 = 2⁶ × 3² × 5¹ × 29¹

Step-3: Factors of 83500

List of positive integer factors of 83500 that divides 83500 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 167, 250, 334, 500, 668, 835, 1670, 3340, 4175, 8350, 16700, 20875, 41750

Step-4: Factors of 83520

List of positive integer factors of 83520 that divides 83500 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 29, 30, 32, 36, 40, 45, 48, 58, 60, 64, 72, 80, 87, 90, 96, 116, 120, 144, 145, 160, 174, 180, 192, 232, 240, 261, 288, 290, 320, 348, 360, 435, 464, 480, 522, 576, 580, 696, 720, 870, 928, 960, 1044, 1160, 1305, 1392, 1440, 1740, 1856, 2088, 2320, 2610, 2784, 2880, 3480, 4176, 4640, 5220, 5568, 6960, 8352, 9280, 10440, 13920, 16704, 20880, 27840, 41760

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 83500 and 83520. The biggest common factor number is the GCF number.
So the greatest common factor 83500 and 83520 is 20.

Also check out the Least Common Multiple of 83500 and 83520