What is the Greatest Common Factor of 83286 and 83300?

Greatest common factor (GCF) of 83286 and 83300 is 14.

GCF(83286,83300) = 14

We will now calculate the prime factors of 83286 and 83300, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 83286 and 83300.

How to find the GCF of 83286 and 83300?

We will first find the prime factorization of 83286 and 83300. After we will calculate the factors of 83286 and 83300 and find the biggest common factor number .

Step-1: Prime Factorization of 83286

Prime factors of 83286 are 2, 3, 7, 661. Prime factorization of 83286 in exponential form is:

83286 = 2¹ × 3² × 7¹ × 661¹

Step-2: Prime Factorization of 83300

Prime factors of 83300 are 2, 5, 7, 17. Prime factorization of 83300 in exponential form is:

83300 = 2² × 5² × 7² × 17¹

Step-3: Factors of 83286

List of positive integer factors of 83286 that divides 83286 without a remainder.

1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126, 661, 1322, 1983, 3966, 4627, 5949, 9254, 11898, 13881, 27762, 41643

Step-4: Factors of 83300

List of positive integer factors of 83300 that divides 83286 without a remainder.

1, 2, 4, 5, 7, 10, 14, 17, 20, 25, 28, 34, 35, 49, 50, 68, 70, 85, 98, 100, 119, 140, 170, 175, 196, 238, 245, 340, 350, 425, 476, 490, 595, 700, 833, 850, 980, 1190, 1225, 1666, 1700, 2380, 2450, 2975, 3332, 4165, 4900, 5950, 8330, 11900, 16660, 20825, 41650

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 83286 and 83300. The biggest common factor number is the GCF number.
So the greatest common factor 83286 and 83300 is 14.

Also check out the Least Common Multiple of 83286 and 83300