What is the Greatest Common Factor of 19738 and 19754?

Greatest common factor (GCF) of 19738 and 19754 is 2.

GCF(19738,19754) = 2

We will now calculate the prime factors of 19738 and 19754, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19738 and 19754.

How to find the GCF of 19738 and 19754?

We will first find the prime factorization of 19738 and 19754. After we will calculate the factors of 19738 and 19754 and find the biggest common factor number .

Step-1: Prime Factorization of 19738

Prime factors of 19738 are 2, 71, 139. Prime factorization of 19738 in exponential form is:

19738 = 2¹ × 71¹ × 139¹

Step-2: Prime Factorization of 19754

Prime factors of 19754 are 2, 7, 17, 83. Prime factorization of 19754 in exponential form is:

19754 = 2¹ × 7¹ × 17¹ × 83¹

Step-3: Factors of 19738

List of positive integer factors of 19738 that divides 19738 without a remainder.

1, 2, 71, 139, 142, 278, 9869

Step-4: Factors of 19754

List of positive integer factors of 19754 that divides 19738 without a remainder.

1, 2, 7, 14, 17, 34, 83, 119, 166, 238, 581, 1162, 1411, 2822, 9877

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19738 and 19754. The biggest common factor number is the GCF number.
So the greatest common factor 19738 and 19754 is 2.

Also check out the Least Common Multiple of 19738 and 19754