What is the Greatest Common Factor of 53184 and 53200?

Greatest common factor (GCF) of 53184 and 53200 is 16.

GCF(53184,53200) = 16

We will now calculate the prime factors of 53184 and 53200, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 53184 and 53200.

How to find the GCF of 53184 and 53200?

We will first find the prime factorization of 53184 and 53200. After we will calculate the factors of 53184 and 53200 and find the biggest common factor number .

Step-1: Prime Factorization of 53184

Prime factors of 53184 are 2, 3, 277. Prime factorization of 53184 in exponential form is:

53184 = 2⁶ × 3¹ × 277¹

Step-2: Prime Factorization of 53200

Prime factors of 53200 are 2, 5, 7, 19. Prime factorization of 53200 in exponential form is:

53200 = 2⁴ × 5² × 7¹ × 19¹

Step-3: Factors of 53184

List of positive integer factors of 53184 that divides 53184 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192, 277, 554, 831, 1108, 1662, 2216, 3324, 4432, 6648, 8864, 13296, 17728, 26592

Step-4: Factors of 53200

List of positive integer factors of 53200 that divides 53184 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 16, 19, 20, 25, 28, 35, 38, 40, 50, 56, 70, 76, 80, 95, 100, 112, 133, 140, 152, 175, 190, 200, 266, 280, 304, 350, 380, 400, 475, 532, 560, 665, 700, 760, 950, 1064, 1330, 1400, 1520, 1900, 2128, 2660, 2800, 3325, 3800, 5320, 6650, 7600, 10640, 13300, 26600

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 53184 and 53200. The biggest common factor number is the GCF number.
So the greatest common factor 53184 and 53200 is 16.

Also check out the Least Common Multiple of 53184 and 53200