What is the Greatest Common Factor of 66300 and 66312?

Greatest common factor (GCF) of 66300 and 66312 is 12.

GCF(66300,66312) = 12

We will now calculate the prime factors of 66300 and 66312, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 66300 and 66312.

How to find the GCF of 66300 and 66312?

We will first find the prime factorization of 66300 and 66312. After we will calculate the factors of 66300 and 66312 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 66312

Prime factors of 66312 are 2, 3, 307. Prime factorization of 66312 in exponential form is:

66312 = 2³ × 3³ × 307¹

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 66312

List of positive integer factors of 66312 that divides 66300 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216, 307, 614, 921, 1228, 1842, 2456, 2763, 3684, 5526, 7368, 8289, 11052, 16578, 22104, 33156

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 66300 and 66312. The biggest common factor number is the GCF number.
So the greatest common factor 66300 and 66312 is 12.

Also check out the Least Common Multiple of 66300 and 66312