What is the Greatest Common Factor of 49104 and 49120?

Greatest common factor (GCF) of 49104 and 49120 is 16.

GCF(49104,49120) = 16

We will now calculate the prime factors of 49104 and 49120, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 49104 and 49120.

How to find the GCF of 49104 and 49120?

We will first find the prime factorization of 49104 and 49120. After we will calculate the factors of 49104 and 49120 and find the biggest common factor number .

Step-1: Prime Factorization of 49104

Prime factors of 49104 are 2, 3, 11, 31. Prime factorization of 49104 in exponential form is:

49104 = 2⁴ × 3² × 11¹ × 31¹

Step-2: Prime Factorization of 49120

Prime factors of 49120 are 2, 5, 307. Prime factorization of 49120 in exponential form is:

49120 = 2⁵ × 5¹ × 307¹

Step-3: Factors of 49104

List of positive integer factors of 49104 that divides 49104 without a remainder.

1, 2, 3, 4, 6, 8, 9, 11, 12, 16, 18, 22, 24, 31, 33, 36, 44, 48, 62, 66, 72, 88, 93, 99, 124, 132, 144, 176, 186, 198, 248, 264, 279, 341, 372, 396, 496, 528, 558, 682, 744, 792, 1023, 1116, 1364, 1488, 1584, 2046, 2232, 2728, 3069, 4092, 4464, 5456, 6138, 8184, 12276, 16368, 24552

Step-4: Factors of 49120

List of positive integer factors of 49120 that divides 49104 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160, 307, 614, 1228, 1535, 2456, 3070, 4912, 6140, 9824, 12280, 24560

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 49104 and 49120. The biggest common factor number is the GCF number.
So the greatest common factor 49104 and 49120 is 16.

Also check out the Least Common Multiple of 49104 and 49120