What is the Greatest Common Factor of 19738 and 19752?

Greatest common factor (GCF) of 19738 and 19752 is 2.

GCF(19738,19752) = 2

We will now calculate the prime factors of 19738 and 19752, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19738 and 19752.

How to find the GCF of 19738 and 19752?

We will first find the prime factorization of 19738 and 19752. After we will calculate the factors of 19738 and 19752 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 19752

Prime factors of 19752 are 2, 3, 823. Prime factorization of 19752 in exponential form is:

19752 = 2³ × 3¹ × 823¹

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 19752

List of positive integer factors of 19752 that divides 19738 without a remainder.

1, 2, 3, 4, 6, 8, 12, 24, 823, 1646, 2469, 3292, 4938, 6584, 9876

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19738 and 19752. The biggest common factor number is the GCF number.
So the greatest common factor 19738 and 19752 is 2.

Also check out the Least Common Multiple of 19738 and 19752