What is the Greatest Common Factor of 66300 and 66314?

Greatest common factor (GCF) of 66300 and 66314 is 2.

GCF(66300,66314) = 2

We will now calculate the prime factors of 66300 and 66314, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 66300 and 66314.

How to find the GCF of 66300 and 66314?

We will first find the prime factorization of 66300 and 66314. After we will calculate the factors of 66300 and 66314 and find the biggest common factor number .

Step-1: Prime Factorization of 66300

Prime factors of 66300 are 2, 3, 5, 13, 17. Prime factorization of 66300 in exponential form is:

66300 = 2² × 3¹ × 5² × 13¹ × 17¹

Step-2: Prime Factorization of 66314

Prime factors of 66314 are 2, 71, 467. Prime factorization of 66314 in exponential form is:

66314 = 2¹ × 71¹ × 467¹

Step-3: Factors of 66300

List of positive integer factors of 66300 that divides 66300 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 17, 20, 25, 26, 30, 34, 39, 50, 51, 52, 60, 65, 68, 75, 78, 85, 100, 102, 130, 150, 156, 170, 195, 204, 221, 255, 260, 300, 325, 340, 390, 425, 442, 510, 650, 663, 780, 850, 884, 975, 1020, 1105, 1275, 1300, 1326, 1700, 1950, 2210, 2550, 2652, 3315, 3900, 4420, 5100, 5525, 6630, 11050, 13260, 16575, 22100, 33150

Step-4: Factors of 66314

List of positive integer factors of 66314 that divides 66300 without a remainder.

1, 2, 71, 142, 467, 934, 33157

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 66300 and 66314. The biggest common factor number is the GCF number.
So the greatest common factor 66300 and 66314 is 2.

Also check out the Least Common Multiple of 66300 and 66314