What is the Greatest Common Factor of 97584 and 97600?

Greatest common factor (GCF) of 97584 and 97600 is 16.

GCF(97584,97600) = 16

We will now calculate the prime factors of 97584 and 97600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 97584 and 97600.

How to find the GCF of 97584 and 97600?

We will first find the prime factorization of 97584 and 97600. After we will calculate the factors of 97584 and 97600 and find the biggest common factor number .

Step-1: Prime Factorization of 97584

Prime factors of 97584 are 2, 3, 19, 107. Prime factorization of 97584 in exponential form is:

97584 = 2⁴ × 3¹ × 19¹ × 107¹

Step-2: Prime Factorization of 97600

Prime factors of 97600 are 2, 5, 61. Prime factorization of 97600 in exponential form is:

97600 = 2⁶ × 5² × 61¹

Step-3: Factors of 97584

List of positive integer factors of 97584 that divides 97584 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 19, 24, 38, 48, 57, 76, 107, 114, 152, 214, 228, 304, 321, 428, 456, 642, 856, 912, 1284, 1712, 2033, 2568, 4066, 5136, 6099, 8132, 12198, 16264, 24396, 32528, 48792

Step-4: Factors of 97600

List of positive integer factors of 97600 that divides 97584 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 61, 64, 80, 100, 122, 160, 200, 244, 305, 320, 400, 488, 610, 800, 976, 1220, 1525, 1600, 1952, 2440, 3050, 3904, 4880, 6100, 9760, 12200, 19520, 24400, 48800

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 97584 and 97600. The biggest common factor number is the GCF number.
So the greatest common factor 97584 and 97600 is 16.

Also check out the Least Common Multiple of 97584 and 97600