What is the Greatest Common Factor of 81305 and 81312?

Greatest common factor (GCF) of 81305 and 81312 is 7.

GCF(81305,81312) = 7

We will now calculate the prime factors of 81305 and 81312, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 81305 and 81312.

How to find the GCF of 81305 and 81312?

We will first find the prime factorization of 81305 and 81312. After we will calculate the factors of 81305 and 81312 and find the biggest common factor number .

Step-1: Prime Factorization of 81305

Prime factors of 81305 are 5, 7, 23, 101. Prime factorization of 81305 in exponential form is:

81305 = 5¹ × 7¹ × 23¹ × 101¹

Step-2: Prime Factorization of 81312

Prime factors of 81312 are 2, 3, 7, 11. Prime factorization of 81312 in exponential form is:

81312 = 2⁵ × 3¹ × 7¹ × 11²

Step-3: Factors of 81305

List of positive integer factors of 81305 that divides 81305 without a remainder.

1, 5, 7, 23, 35, 101, 115, 161, 505, 707, 805, 2323, 3535, 11615, 16261

Step-4: Factors of 81312

List of positive integer factors of 81312 that divides 81305 without a remainder.

1, 2, 3, 4, 6, 7, 8, 11, 12, 14, 16, 21, 22, 24, 28, 32, 33, 42, 44, 48, 56, 66, 77, 84, 88, 96, 112, 121, 132, 154, 168, 176, 224, 231, 242, 264, 308, 336, 352, 363, 462, 484, 528, 616, 672, 726, 847, 924, 968, 1056, 1232, 1452, 1694, 1848, 1936, 2464, 2541, 2904, 3388, 3696, 3872, 5082, 5808, 6776, 7392, 10164, 11616, 13552, 20328, 27104, 40656

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 81305 and 81312. The biggest common factor number is the GCF number.
So the greatest common factor 81305 and 81312 is 7.

Also check out the Least Common Multiple of 81305 and 81312