What is the Greatest Common Factor of 19747 and 19760?

Greatest common factor (GCF) of 19747 and 19760 is 13.

GCF(19747,19760) = 13

We will now calculate the prime factors of 19747 and 19760, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 19747 and 19760.

How to find the GCF of 19747 and 19760?

We will first find the prime factorization of 19747 and 19760. After we will calculate the factors of 19747 and 19760 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 19760

Prime factors of 19760 are 2, 5, 13, 19. Prime factorization of 19760 in exponential form is:

19760 = 2⁴ × 5¹ × 13¹ × 19¹

Step-3: Factors of 19747

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

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

Step-4: Factors of 19760

List of positive integer factors of 19760 that divides 19747 without a remainder.

1, 2, 4, 5, 8, 10, 13, 16, 19, 20, 26, 38, 40, 52, 65, 76, 80, 95, 104, 130, 152, 190, 208, 247, 260, 304, 380, 494, 520, 760, 988, 1040, 1235, 1520, 1976, 2470, 3952, 4940, 9880

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 19747 and 19760. The biggest common factor number is the GCF number.
So the greatest common factor 19747 and 19760 is 13.

Also check out the Least Common Multiple of 19747 and 19760