What is the Greatest Common Factor of 49184 and 49200?

Greatest common factor (GCF) of 49184 and 49200 is 16.

GCF(49184,49200) = 16

We will now calculate the prime factors of 49184 and 49200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 49184 and 49200.

How to find the GCF of 49184 and 49200?

We will first find the prime factorization of 49184 and 49200. After we will calculate the factors of 49184 and 49200 and find the biggest common factor number .

Step-1: Prime Factorization of 49184

Prime factors of 49184 are 2, 29, 53. Prime factorization of 49184 in exponential form is:

49184 = 2⁵ × 29¹ × 53¹

Step-2: Prime Factorization of 49200

Prime factors of 49200 are 2, 3, 5, 41. Prime factorization of 49200 in exponential form is:

49200 = 2⁴ × 3¹ × 5² × 41¹

Step-3: Factors of 49184

List of positive integer factors of 49184 that divides 49184 without a remainder.

1, 2, 4, 8, 16, 29, 32, 53, 58, 106, 116, 212, 232, 424, 464, 848, 928, 1537, 1696, 3074, 6148, 12296, 24592

Step-4: Factors of 49200

List of positive integer factors of 49200 that divides 49184 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 41, 48, 50, 60, 75, 80, 82, 100, 120, 123, 150, 164, 200, 205, 240, 246, 300, 328, 400, 410, 492, 600, 615, 656, 820, 984, 1025, 1200, 1230, 1640, 1968, 2050, 2460, 3075, 3280, 4100, 4920, 6150, 8200, 9840, 12300, 16400, 24600

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 49184 and 49200. The biggest common factor number is the GCF number.
So the greatest common factor 49184 and 49200 is 16.

Also check out the Least Common Multiple of 49184 and 49200