What is the Greatest Common Factor of 49152 and 49170?

Greatest common factor (GCF) of 49152 and 49170 is 6.

GCF(49152,49170) = 6

We will now calculate the prime factors of 49152 and 49170, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 49152 and 49170.

How to find the GCF of 49152 and 49170?

We will first find the prime factorization of 49152 and 49170. After we will calculate the factors of 49152 and 49170 and find the biggest common factor number .

Step-1: Prime Factorization of 49152

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

49152 = 2¹⁴ × 3¹

Step-2: Prime Factorization of 49170

Prime factors of 49170 are 2, 3, 5, 11, 149. Prime factorization of 49170 in exponential form is:

49170 = 2¹ × 3¹ × 5¹ × 11¹ × 149¹

Step-3: Factors of 49152

List of positive integer factors of 49152 that divides 49152 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

Step-4: Factors of 49170

List of positive integer factors of 49170 that divides 49152 without a remainder.

1, 2, 3, 5, 6, 10, 11, 15, 22, 30, 33, 55, 66, 110, 149, 165, 298, 330, 447, 745, 894, 1490, 1639, 2235, 3278, 4470, 4917, 8195, 9834, 16390, 24585

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 49152 and 49170. The biggest common factor number is the GCF number.
So the greatest common factor 49152 and 49170 is 6.

Also check out the Least Common Multiple of 49152 and 49170