What is the Greatest Common Factor of 97280 and 97300?

Greatest common factor (GCF) of 97280 and 97300 is 20.

GCF(97280,97300) = 20

We will now calculate the prime factors of 97280 and 97300, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 97280 and 97300.

How to find the GCF of 97280 and 97300?

We will first find the prime factorization of 97280 and 97300. After we will calculate the factors of 97280 and 97300 and find the biggest common factor number .

Step-1: Prime Factorization of 97280

Prime factors of 97280 are 2, 5, 19. Prime factorization of 97280 in exponential form is:

97280 = 2¹⁰ × 5¹ × 19¹

Step-2: Prime Factorization of 97300

Prime factors of 97300 are 2, 5, 7, 139. Prime factorization of 97300 in exponential form is:

97300 = 2² × 5² × 7¹ × 139¹

Step-3: Factors of 97280

List of positive integer factors of 97280 that divides 97280 without a remainder.

1, 2, 4, 5, 8, 10, 16, 19, 20, 32, 38, 40, 64, 76, 80, 95, 128, 152, 160, 190, 256, 304, 320, 380, 512, 608, 640, 760, 1024, 1216, 1280, 1520, 2432, 2560, 3040, 4864, 5120, 6080, 9728, 12160, 19456, 24320, 48640

Step-4: Factors of 97300

List of positive integer factors of 97300 that divides 97280 without a remainder.

1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 139, 140, 175, 278, 350, 556, 695, 700, 973, 1390, 1946, 2780, 3475, 3892, 4865, 6950, 9730, 13900, 19460, 24325, 48650

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 97280 and 97300. The biggest common factor number is the GCF number.
So the greatest common factor 97280 and 97300 is 20.

Also check out the Least Common Multiple of 97280 and 97300