What is the Greatest Common Factor of 1700 and 1710?

Greatest common factor (GCF) of 1700 and 1710 is 10.

GCF(1700,1710) = 10

We will now calculate the prime factors of 1700 and 1710, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1700 and 1710.

How to find the GCF of 1700 and 1710?

We will first find the prime factorization of 1700 and 1710. After we will calculate the factors of 1700 and 1710 and find the biggest common factor number .

Step-1: Prime Factorization of 1700

Prime factors of 1700 are 2, 5, 17. Prime factorization of 1700 in exponential form is:

1700 = 2² × 5² × 17¹

Step-2: 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-3: Factors of 1700

List of positive integer factors of 1700 that divides 1700 without a remainder.

1, 2, 4, 5, 10, 17, 20, 25, 34, 50, 68, 85, 100, 170, 340, 425, 850

Step-4: Factors of 1710

List of positive integer factors of 1710 that divides 1700 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1700 and 1710. The biggest common factor number is the GCF number.
So the greatest common factor 1700 and 1710 is 10.

Also check out the Least Common Multiple of 1700 and 1710