What is the Greatest Common Factor of 19754 and 19768?

Greatest common factor (GCF) of 19754 and 19768 is 14.

GCF(19754,19768) = 14

We will now calculate the prime factors of 19754 and 19768, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19754 and 19768.

How to find the GCF of 19754 and 19768?

We will first find the prime factorization of 19754 and 19768. After we will calculate the factors of 19754 and 19768 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 19768

Prime factors of 19768 are 2, 7, 353. Prime factorization of 19768 in exponential form is:

19768 = 2³ × 7¹ × 353¹

Step-3: Factors of 19754

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

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

Step-4: Factors of 19768

List of positive integer factors of 19768 that divides 19754 without a remainder.

1, 2, 4, 7, 8, 14, 28, 56, 353, 706, 1412, 2471, 2824, 4942, 9884

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19754 and 19768. The biggest common factor number is the GCF number.
So the greatest common factor 19754 and 19768 is 14.

Also check out the Least Common Multiple of 19754 and 19768