What is the Greatest Common Factor of 69303 and 69312?

Greatest common factor (GCF) of 69303 and 69312 is 3.

GCF(69303,69312) = 3

We will now calculate the prime factors of 69303 and 69312, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 69303 and 69312.

How to find the GCF of 69303 and 69312?

We will first find the prime factorization of 69303 and 69312. After we will calculate the factors of 69303 and 69312 and find the biggest common factor number .

Step-1: Prime Factorization of 69303

Prime factors of 69303 are 3, 13, 1777. Prime factorization of 69303 in exponential form is:

69303 = 3¹ × 13¹ × 1777¹

Step-2: Prime Factorization of 69312

Prime factors of 69312 are 2, 3, 19. Prime factorization of 69312 in exponential form is:

69312 = 2⁶ × 3¹ × 19²

Step-3: Factors of 69303

List of positive integer factors of 69303 that divides 69303 without a remainder.

1, 3, 13, 39, 1777, 5331, 23101

Step-4: Factors of 69312

List of positive integer factors of 69312 that divides 69303 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 19, 24, 32, 38, 48, 57, 64, 76, 96, 114, 152, 192, 228, 304, 361, 456, 608, 722, 912, 1083, 1216, 1444, 1824, 2166, 2888, 3648, 4332, 5776, 8664, 11552, 17328, 23104, 34656

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 69303 and 69312. The biggest common factor number is the GCF number.
So the greatest common factor 69303 and 69312 is 3.

Also check out the Least Common Multiple of 69303 and 69312