What is the Greatest Common Factor of 19120 and 19138?

Greatest common factor (GCF) of 19120 and 19138 is 2.

GCF(19120,19138) = 2

We will now calculate the prime factors of 19120 and 19138, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19120 and 19138.

How to find the GCF of 19120 and 19138?

We will first find the prime factorization of 19120 and 19138. After we will calculate the factors of 19120 and 19138 and find the biggest common factor number .

Step-1: Prime Factorization of 19120

Prime factors of 19120 are 2, 5, 239. Prime factorization of 19120 in exponential form is:

19120 = 2⁴ × 5¹ × 239¹

Step-2: Prime Factorization of 19138

Prime factors of 19138 are 2, 7, 1367. Prime factorization of 19138 in exponential form is:

19138 = 2¹ × 7¹ × 1367¹

Step-3: Factors of 19120

List of positive integer factors of 19120 that divides 19120 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 40, 80, 239, 478, 956, 1195, 1912, 2390, 3824, 4780, 9560

Step-4: Factors of 19138

List of positive integer factors of 19138 that divides 19120 without a remainder.

1, 2, 7, 14, 1367, 2734, 9569

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19120 and 19138. The biggest common factor number is the GCF number.
So the greatest common factor 19120 and 19138 is 2.

Also check out the Least Common Multiple of 19120 and 19138