What is the Greatest Common Factor of 49776 and 49792?

Greatest common factor (GCF) of 49776 and 49792 is 16.

GCF(49776,49792) = 16

We will now calculate the prime factors of 49776 and 49792, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 49776 and 49792.

How to find the GCF of 49776 and 49792?

We will first find the prime factorization of 49776 and 49792. After we will calculate the factors of 49776 and 49792 and find the biggest common factor number .

Step-1: Prime Factorization of 49776

Prime factors of 49776 are 2, 3, 17, 61. Prime factorization of 49776 in exponential form is:

49776 = 2⁴ × 3¹ × 17¹ × 61¹

Step-2: Prime Factorization of 49792

Prime factors of 49792 are 2, 389. Prime factorization of 49792 in exponential form is:

49792 = 2⁷ × 389¹

Step-3: Factors of 49776

List of positive integer factors of 49776 that divides 49776 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 17, 24, 34, 48, 51, 61, 68, 102, 122, 136, 183, 204, 244, 272, 366, 408, 488, 732, 816, 976, 1037, 1464, 2074, 2928, 3111, 4148, 6222, 8296, 12444, 16592, 24888

Step-4: Factors of 49792

List of positive integer factors of 49792 that divides 49776 without a remainder.

1, 2, 4, 8, 16, 32, 64, 128, 389, 778, 1556, 3112, 6224, 12448, 24896

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 49776 and 49792. The biggest common factor number is the GCF number.
So the greatest common factor 49776 and 49792 is 16.

Also check out the Least Common Multiple of 49776 and 49792