What is the Greatest Common Factor of 19754 and 19771?

Greatest common factor (GCF) of 19754 and 19771 is 17.

GCF(19754,19771) = 17

We will now calculate the prime factors of 19754 and 19771, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19754 and 19771.

How to find the GCF of 19754 and 19771?

We will first find the prime factorization of 19754 and 19771. After we will calculate the factors of 19754 and 19771 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 19771

Prime factors of 19771 are 17, 1163. Prime factorization of 19771 in exponential form is:

19771 = 17¹ × 1163¹

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 19771

List of positive integer factors of 19771 that divides 19754 without a remainder.

1, 17, 1163

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19754 and 19771. The biggest common factor number is the GCF number.
So the greatest common factor 19754 and 19771 is 17.

Also check out the Least Common Multiple of 19754 and 19771