What is the Greatest Common Factor of 28736 and 28742?

Greatest common factor (GCF) of 28736 and 28742 is 2.

GCF(28736,28742) = 2

We will now calculate the prime factors of 28736 and 28742, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 28736 and 28742.

How to find the GCF of 28736 and 28742?

We will first find the prime factorization of 28736 and 28742. After we will calculate the factors of 28736 and 28742 and find the biggest common factor number .

Step-1: Prime Factorization of 28736

Prime factors of 28736 are 2, 449. Prime factorization of 28736 in exponential form is:

28736 = 2⁶ × 449¹

Step-2: Prime Factorization of 28742

Prime factors of 28742 are 2, 7, 2053. Prime factorization of 28742 in exponential form is:

28742 = 2¹ × 7¹ × 2053¹

Step-3: Factors of 28736

List of positive integer factors of 28736 that divides 28736 without a remainder.

1, 2, 4, 8, 16, 32, 64, 449, 898, 1796, 3592, 7184, 14368

Step-4: Factors of 28742

List of positive integer factors of 28742 that divides 28736 without a remainder.

1, 2, 7, 14, 2053, 4106, 14371

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 28736 and 28742. The biggest common factor number is the GCF number.
So the greatest common factor 28736 and 28742 is 2.

Also check out the Least Common Multiple of 28736 and 28742