What is the Greatest Common Factor of 83300 and 83314?

Greatest common factor (GCF) of 83300 and 83314 is 14.

GCF(83300,83314) = 14

We will now calculate the prime factors of 83300 and 83314, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 83300 and 83314.

How to find the GCF of 83300 and 83314?

We will first find the prime factorization of 83300 and 83314. After we will calculate the factors of 83300 and 83314 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 83314

Prime factors of 83314 are 2, 7, 11, 541. Prime factorization of 83314 in exponential form is:

83314 = 2¹ × 7¹ × 11¹ × 541¹

Step-3: Factors of 83300

List of positive integer factors of 83300 that divides 83300 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

Step-4: Factors of 83314

List of positive integer factors of 83314 that divides 83300 without a remainder.

1, 2, 7, 11, 14, 22, 77, 154, 541, 1082, 3787, 5951, 7574, 11902, 41657

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 83300 and 83314. The biggest common factor number is the GCF number.
So the greatest common factor 83300 and 83314 is 14.

Also check out the Least Common Multiple of 83300 and 83314