What is the Greatest Common Factor of 19600 and 19610?

Greatest common factor (GCF) of 19600 and 19610 is 10.

GCF(19600,19610) = 10

We will now calculate the prime factors of 19600 and 19610, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19600 and 19610.

How to find the GCF of 19600 and 19610?

We will first find the prime factorization of 19600 and 19610. After we will calculate the factors of 19600 and 19610 and find the biggest common factor number .

Step-1: Prime Factorization of 19600

Prime factors of 19600 are 2, 5, 7. Prime factorization of 19600 in exponential form is:

19600 = 2⁴ × 5² × 7²

Step-2: Prime Factorization of 19610

Prime factors of 19610 are 2, 5, 37, 53. Prime factorization of 19610 in exponential form is:

19610 = 2¹ × 5¹ × 37¹ × 53¹

Step-3: Factors of 19600

List of positive integer factors of 19600 that divides 19600 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 25, 28, 35, 40, 49, 50, 56, 70, 80, 98, 100, 112, 140, 175, 196, 200, 245, 280, 350, 392, 400, 490, 560, 700, 784, 980, 1225, 1400, 1960, 2450, 2800, 3920, 4900, 9800

Step-4: Factors of 19610

List of positive integer factors of 19610 that divides 19600 without a remainder.

1, 2, 5, 10, 37, 53, 74, 106, 185, 265, 370, 530, 1961, 3922, 9805

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19600 and 19610. The biggest common factor number is the GCF number.
So the greatest common factor 19600 and 19610 is 10.

Also check out the Least Common Multiple of 19600 and 19610