What is the Greatest Common Factor of 77728 and 77742?

Greatest common factor (GCF) of 77728 and 77742 is 14.

GCF(77728,77742) = 14

We will now calculate the prime factors of 77728 and 77742, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 77728 and 77742.

How to find the GCF of 77728 and 77742?

We will first find the prime factorization of 77728 and 77742. After we will calculate the factors of 77728 and 77742 and find the biggest common factor number .

Step-1: Prime Factorization of 77728

Prime factors of 77728 are 2, 7, 347. Prime factorization of 77728 in exponential form is:

77728 = 2⁵ × 7¹ × 347¹

Step-2: Prime Factorization of 77742

Prime factors of 77742 are 2, 3, 7, 617. Prime factorization of 77742 in exponential form is:

77742 = 2¹ × 3² × 7¹ × 617¹

Step-3: Factors of 77728

List of positive integer factors of 77728 that divides 77728 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 112, 224, 347, 694, 1388, 2429, 2776, 4858, 5552, 9716, 11104, 19432, 38864

Step-4: Factors of 77742

List of positive integer factors of 77742 that divides 77728 without a remainder.

1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126, 617, 1234, 1851, 3702, 4319, 5553, 8638, 11106, 12957, 25914, 38871

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 77728 and 77742. The biggest common factor number is the GCF number.
So the greatest common factor 77728 and 77742 is 14.

Also check out the Least Common Multiple of 77728 and 77742