What is the Greatest Common Factor of 1710 and 1729?

Greatest common factor (GCF) of 1710 and 1729 is 19.

GCF(1710,1729) = 19

We will now calculate the prime factors of 1710 and 1729, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1710 and 1729.

How to find the GCF of 1710 and 1729?

We will first find the prime factorization of 1710 and 1729. After we will calculate the factors of 1710 and 1729 and find the biggest common factor number .

Step-1: Prime Factorization of 1710

Prime factors of 1710 are 2, 3, 5, 19. Prime factorization of 1710 in exponential form is:

1710 = 2¹ × 3² × 5¹ × 19¹

Step-2: Prime Factorization of 1729

Prime factors of 1729 are 7, 13, 19. Prime factorization of 1729 in exponential form is:

1729 = 7¹ × 13¹ × 19¹

Step-3: Factors of 1710

List of positive integer factors of 1710 that divides 1710 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 19, 30, 38, 45, 57, 90, 95, 114, 171, 190, 285, 342, 570, 855

Step-4: Factors of 1729

List of positive integer factors of 1729 that divides 1710 without a remainder.

1, 7, 13, 19, 91, 133, 247

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1710 and 1729. The biggest common factor number is the GCF number.
So the greatest common factor 1710 and 1729 is 19.

Also check out the Least Common Multiple of 1710 and 1729