What is the Greatest Common Factor of 53138 and 53152?

Greatest common factor (GCF) of 53138 and 53152 is 2.

GCF(53138,53152) = 2

We will now calculate the prime factors of 53138 and 53152, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 53138 and 53152.

How to find the GCF of 53138 and 53152?

We will first find the prime factorization of 53138 and 53152. After we will calculate the factors of 53138 and 53152 and find the biggest common factor number .

Step-1: Prime Factorization of 53138

Prime factors of 53138 are 2, 163. Prime factorization of 53138 in exponential form is:

53138 = 2¹ × 163²

Step-2: Prime Factorization of 53152

Prime factors of 53152 are 2, 11, 151. Prime factorization of 53152 in exponential form is:

53152 = 2⁵ × 11¹ × 151¹

Step-3: Factors of 53138

List of positive integer factors of 53138 that divides 53138 without a remainder.

1, 2, 163, 326, 26569

Step-4: Factors of 53152

List of positive integer factors of 53152 that divides 53138 without a remainder.

1, 2, 4, 8, 11, 16, 22, 32, 44, 88, 151, 176, 302, 352, 604, 1208, 1661, 2416, 3322, 4832, 6644, 13288, 26576

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 53138 and 53152. The biggest common factor number is the GCF number.
So the greatest common factor 53138 and 53152 is 2.

Also check out the Least Common Multiple of 53138 and 53152