What is the Greatest Common Factor of 69296 and 69312?

Greatest common factor (GCF) of 69296 and 69312 is 16.

GCF(69296,69312) = 16

We will now calculate the prime factors of 69296 and 69312, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 69296 and 69312.

How to find the GCF of 69296 and 69312?

We will first find the prime factorization of 69296 and 69312. After we will calculate the factors of 69296 and 69312 and find the biggest common factor number .

Step-1: Prime Factorization of 69296

Prime factors of 69296 are 2, 61, 71. Prime factorization of 69296 in exponential form is:

69296 = 2⁴ × 61¹ × 71¹

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 69296

List of positive integer factors of 69296 that divides 69296 without a remainder.

1, 2, 4, 8, 16, 61, 71, 122, 142, 244, 284, 488, 568, 976, 1136, 4331, 8662, 17324, 34648

Step-4: Factors of 69312

List of positive integer factors of 69312 that divides 69296 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 69296 and 69312. The biggest common factor number is the GCF number.
So the greatest common factor 69296 and 69312 is 16.

Also check out the Least Common Multiple of 69296 and 69312