What is the Greatest Common Factor of 19600 and 19608?

Greatest common factor (GCF) of 19600 and 19608 is 8.

GCF(19600,19608) = 8

We will now calculate the prime factors of 19600 and 19608, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19600 and 19608.

How to find the GCF of 19600 and 19608?

We will first find the prime factorization of 19600 and 19608. After we will calculate the factors of 19600 and 19608 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 19608

Prime factors of 19608 are 2, 3, 19, 43. Prime factorization of 19608 in exponential form is:

19608 = 2³ × 3¹ × 19¹ × 43¹

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 19608

List of positive integer factors of 19608 that divides 19600 without a remainder.

1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 43, 57, 76, 86, 114, 129, 152, 172, 228, 258, 344, 456, 516, 817, 1032, 1634, 2451, 3268, 4902, 6536, 9804

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19600 and 19608. The biggest common factor number is the GCF number.
So the greatest common factor 19600 and 19608 is 8.

Also check out the Least Common Multiple of 19600 and 19608