What is the Greatest Common Factor of 19737 and 19754?

Greatest common factor (GCF) of 19737 and 19754 is 17.

GCF(19737,19754) = 17

We will now calculate the prime factors of 19737 and 19754, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19737 and 19754.

How to find the GCF of 19737 and 19754?

We will first find the prime factorization of 19737 and 19754. After we will calculate the factors of 19737 and 19754 and find the biggest common factor number .

Step-1: Prime Factorization of 19737

Prime factors of 19737 are 3, 17, 43. Prime factorization of 19737 in exponential form is:

19737 = 3³ × 17¹ × 43¹

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 19737

List of positive integer factors of 19737 that divides 19737 without a remainder.

1, 3, 9, 17, 27, 43, 51, 129, 153, 387, 459, 731, 1161, 2193, 6579

Step-4: Factors of 19754

List of positive integer factors of 19754 that divides 19737 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 19737 and 19754. The biggest common factor number is the GCF number.
So the greatest common factor 19737 and 19754 is 17.

Also check out the Least Common Multiple of 19737 and 19754