What is the Greatest Common Factor of 97200 and 97209?

Greatest common factor (GCF) of 97200 and 97209 is 9.

GCF(97200,97209) = 9

We will now calculate the prime factors of 97200 and 97209, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 97200 and 97209.

How to find the GCF of 97200 and 97209?

We will first find the prime factorization of 97200 and 97209. After we will calculate the factors of 97200 and 97209 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 97209

Prime factors of 97209 are 3, 7, 1543. Prime factorization of 97209 in exponential form is:

97209 = 3² × 7¹ × 1543¹

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 97209

List of positive integer factors of 97209 that divides 97200 without a remainder.

1, 3, 7, 9, 21, 63, 1543, 4629, 10801, 13887, 32403

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 97200 and 97209. The biggest common factor number is the GCF number.
So the greatest common factor 97200 and 97209 is 9.

Also check out the Least Common Multiple of 97200 and 97209