What is the Greatest Common Factor of 45728 and 45738?

Greatest common factor (GCF) of 45728 and 45738 is 2.

GCF(45728,45738) = 2

We will now calculate the prime factors of 45728 and 45738, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 45728 and 45738.

How to find the GCF of 45728 and 45738?

We will first find the prime factorization of 45728 and 45738. After we will calculate the factors of 45728 and 45738 and find the biggest common factor number .

Step-1: Prime Factorization of 45728

Prime factors of 45728 are 2, 1429. Prime factorization of 45728 in exponential form is:

45728 = 2⁵ × 1429¹

Step-2: Prime Factorization of 45738

Prime factors of 45738 are 2, 3, 7, 11. Prime factorization of 45738 in exponential form is:

45738 = 2¹ × 3³ × 7¹ × 11²

Step-3: Factors of 45728

List of positive integer factors of 45728 that divides 45728 without a remainder.

1, 2, 4, 8, 16, 32, 1429, 2858, 5716, 11432, 22864

Step-4: Factors of 45738

List of positive integer factors of 45738 that divides 45728 without a remainder.

1, 2, 3, 6, 7, 9, 11, 14, 18, 21, 22, 27, 33, 42, 54, 63, 66, 77, 99, 121, 126, 154, 189, 198, 231, 242, 297, 363, 378, 462, 594, 693, 726, 847, 1089, 1386, 1694, 2079, 2178, 2541, 3267, 4158, 5082, 6534, 7623, 15246, 22869

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 45728 and 45738. The biggest common factor number is the GCF number.
So the greatest common factor 45728 and 45738 is 2.

Also check out the Least Common Multiple of 45728 and 45738