What is the Greatest Common Factor of 9709 and 9728?

Greatest common factor (GCF) of 9709 and 9728 is 19.

GCF(9709,9728) = 19

We will now calculate the prime factors of 9709 and 9728, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 9709 and 9728.

How to find the GCF of 9709 and 9728?

We will first find the prime factorization of 9709 and 9728. After we will calculate the factors of 9709 and 9728 and find the biggest common factor number .

Step-1: Prime Factorization of 9709

Prime factors of 9709 are 7, 19, 73. Prime factorization of 9709 in exponential form is:

9709 = 7¹ × 19¹ × 73¹

Step-2: Prime Factorization of 9728

Prime factors of 9728 are 2, 19. Prime factorization of 9728 in exponential form is:

9728 = 2⁹ × 19¹

Step-3: Factors of 9709

List of positive integer factors of 9709 that divides 9709 without a remainder.

1, 7, 19, 73, 133, 511, 1387

Step-4: Factors of 9728

List of positive integer factors of 9728 that divides 9709 without a remainder.

1, 2, 4, 8, 16, 19, 32, 38, 64, 76, 128, 152, 256, 304, 512, 608, 1216, 2432, 4864

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 9709 and 9728. The biggest common factor number is the GCF number.
So the greatest common factor 9709 and 9728 is 19.

Also check out the Least Common Multiple of 9709 and 9728