What is the Greatest Common Factor of 28728 and 28742?

Greatest common factor (GCF) of 28728 and 28742 is 14.

GCF(28728,28742) = 14

We will now calculate the prime factors of 28728 and 28742, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 28728 and 28742.

How to find the GCF of 28728 and 28742?

We will first find the prime factorization of 28728 and 28742. After we will calculate the factors of 28728 and 28742 and find the biggest common factor number .

Step-1: Prime Factorization of 28728

Prime factors of 28728 are 2, 3, 7, 19. Prime factorization of 28728 in exponential form is:

28728 = 2³ × 3³ × 7¹ × 19¹

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 28728

List of positive integer factors of 28728 that divides 28728 without a remainder.

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 19, 21, 24, 27, 28, 36, 38, 42, 54, 56, 57, 63, 72, 76, 84, 108, 114, 126, 133, 152, 168, 171, 189, 216, 228, 252, 266, 342, 378, 399, 456, 504, 513, 532, 684, 756, 798, 1026, 1064, 1197, 1368, 1512, 1596, 2052, 2394, 3192, 3591, 4104, 4788, 7182, 9576, 14364

Step-4: Factors of 28742

List of positive integer factors of 28742 that divides 28728 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 28728 and 28742. The biggest common factor number is the GCF number.
So the greatest common factor 28728 and 28742 is 14.

Also check out the Least Common Multiple of 28728 and 28742