What is the Greatest Common Factor of 97200 and 97216?

Greatest common factor (GCF) of 97200 and 97216 is 16.

GCF(97200,97216) = 16

We will now calculate the prime factors of 97200 and 97216, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 97200 and 97216.

How to find the GCF of 97200 and 97216?

We will first find the prime factorization of 97200 and 97216. After we will calculate the factors of 97200 and 97216 and find the biggest common factor number .

Step-1: Prime Factorization of 97200

Prime factors of 97200 are 2, 3, 5. Prime factorization of 97200 in exponential form is:

97200 = 2⁴ × 3⁵ × 5²

Step-2: Prime Factorization of 97216

Prime factors of 97216 are 2, 7, 31. Prime factorization of 97216 in exponential form is:

97216 = 2⁶ × 7² × 31¹

Step-3: Factors of 97200

List of positive integer factors of 97200 that divides 97200 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 36, 40, 45, 48, 50, 54, 60, 72, 75, 80, 81, 90, 100, 108, 120, 135, 144, 150, 162, 180, 200, 216, 225, 240, 243, 270, 300, 324, 360, 400, 405, 432, 450, 486, 540, 600, 648, 675, 720, 810, 900, 972, 1080, 1200, 1215, 1296, 1350, 1620, 1800, 1944, 2025, 2160, 2430, 2700, 3240, 3600, 3888, 4050, 4860, 5400, 6075, 6480, 8100, 9720, 10800, 12150, 16200, 19440, 24300, 32400, 48600

Step-4: Factors of 97216

List of positive integer factors of 97216 that divides 97200 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 31, 32, 49, 56, 62, 64, 98, 112, 124, 196, 217, 224, 248, 392, 434, 448, 496, 784, 868, 992, 1519, 1568, 1736, 1984, 3038, 3136, 3472, 6076, 6944, 12152, 13888, 24304, 48608

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 97200 and 97216. The biggest common factor number is the GCF number.
So the greatest common factor 97200 and 97216 is 16.

Also check out the Least Common Multiple of 97200 and 97216