What is the Greatest Common Factor of 28735 and 28749?

Greatest common factor (GCF) of 28735 and 28749 is 7.

GCF(28735,28749) = 7

We will now calculate the prime factors of 28735 and 28749, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 28735 and 28749.

How to find the GCF of 28735 and 28749?

We will first find the prime factorization of 28735 and 28749. After we will calculate the factors of 28735 and 28749 and find the biggest common factor number .

Step-1: Prime Factorization of 28735

Prime factors of 28735 are 5, 7, 821. Prime factorization of 28735 in exponential form is:

28735 = 5¹ × 7¹ × 821¹

Step-2: Prime Factorization of 28749

Prime factors of 28749 are 3, 7, 37. Prime factorization of 28749 in exponential form is:

28749 = 3¹ × 7¹ × 37²

Step-3: Factors of 28735

List of positive integer factors of 28735 that divides 28735 without a remainder.

1, 5, 7, 35, 821, 4105, 5747

Step-4: Factors of 28749

List of positive integer factors of 28749 that divides 28735 without a remainder.

1, 3, 7, 21, 37, 111, 259, 777, 1369, 4107, 9583

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 28735 and 28749. The biggest common factor number is the GCF number.
So the greatest common factor 28735 and 28749 is 7.

Also check out the Least Common Multiple of 28735 and 28749