What is the Greatest Common Factor of 49136 and 49152?

Greatest common factor (GCF) of 49136 and 49152 is 16.

GCF(49136,49152) = 16

We will now calculate the prime factors of 49136 and 49152, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 49136 and 49152.

How to find the GCF of 49136 and 49152?

We will first find the prime factorization of 49136 and 49152. After we will calculate the factors of 49136 and 49152 and find the biggest common factor number .

Step-1: Prime Factorization of 49136

Prime factors of 49136 are 2, 37, 83. Prime factorization of 49136 in exponential form is:

49136 = 2⁴ × 37¹ × 83¹

Step-2: Prime Factorization of 49152

Prime factors of 49152 are 2, 3. Prime factorization of 49152 in exponential form is:

49152 = 2¹⁴ × 3¹

Step-3: Factors of 49136

List of positive integer factors of 49136 that divides 49136 without a remainder.

1, 2, 4, 8, 16, 37, 74, 83, 148, 166, 296, 332, 592, 664, 1328, 3071, 6142, 12284, 24568

Step-4: Factors of 49152

List of positive integer factors of 49152 that divides 49136 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 512, 768, 1024, 1536, 2048, 3072, 4096, 6144, 8192, 12288, 16384, 24576

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 49136 and 49152. The biggest common factor number is the GCF number.
So the greatest common factor 49136 and 49152 is 16.

Also check out the Least Common Multiple of 49136 and 49152