What is the Greatest Common Factor of 19734 and 19747?

Greatest common factor (GCF) of 19734 and 19747 is 13.

GCF(19734,19747) = 13

We will now calculate the prime factors of 19734 and 19747, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19734 and 19747.

How to find the GCF of 19734 and 19747?

We will first find the prime factorization of 19734 and 19747. After we will calculate the factors of 19734 and 19747 and find the biggest common factor number .

Step-1: Prime Factorization of 19734

Prime factors of 19734 are 2, 3, 11, 13, 23. Prime factorization of 19734 in exponential form is:

19734 = 2¹ × 3¹ × 11¹ × 13¹ × 23¹

Step-2: Prime Factorization of 19747

Prime factors of 19747 are 7, 13, 31. Prime factorization of 19747 in exponential form is:

19747 = 7² × 13¹ × 31¹

Step-3: Factors of 19734

List of positive integer factors of 19734 that divides 19734 without a remainder.

1, 2, 3, 6, 11, 13, 22, 23, 26, 33, 39, 46, 66, 69, 78, 138, 143, 253, 286, 299, 429, 506, 598, 759, 858, 897, 1518, 1794, 3289, 6578, 9867

Step-4: Factors of 19747

List of positive integer factors of 19747 that divides 19734 without a remainder.

1, 7, 13, 31, 49, 91, 217, 403, 637, 1519, 2821

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19734 and 19747. The biggest common factor number is the GCF number.
So the greatest common factor 19734 and 19747 is 13.

Also check out the Least Common Multiple of 19734 and 19747