What is the Greatest Common Factor of 17700 and 17710?

Greatest common factor (GCF) of 17700 and 17710 is 10.

GCF(17700,17710) = 10

We will now calculate the prime factors of 17700 and 17710, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17700 and 17710.

How to find the GCF of 17700 and 17710?

We will first find the prime factorization of 17700 and 17710. After we will calculate the factors of 17700 and 17710 and find the biggest common factor number .

Step-1: Prime Factorization of 17700

Prime factors of 17700 are 2, 3, 5, 59. Prime factorization of 17700 in exponential form is:

17700 = 2² × 3¹ × 5² × 59¹

Step-2: Prime Factorization of 17710

Prime factors of 17710 are 2, 5, 7, 11, 23. Prime factorization of 17710 in exponential form is:

17710 = 2¹ × 5¹ × 7¹ × 11¹ × 23¹

Step-3: Factors of 17700

List of positive integer factors of 17700 that divides 17700 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 59, 60, 75, 100, 118, 150, 177, 236, 295, 300, 354, 590, 708, 885, 1180, 1475, 1770, 2950, 3540, 4425, 5900, 8850

Step-4: Factors of 17710

List of positive integer factors of 17710 that divides 17700 without a remainder.

1, 2, 5, 7, 10, 11, 14, 22, 23, 35, 46, 55, 70, 77, 110, 115, 154, 161, 230, 253, 322, 385, 506, 770, 805, 1265, 1610, 1771, 2530, 3542, 8855

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17700 and 17710. The biggest common factor number is the GCF number.
So the greatest common factor 17700 and 17710 is 10.

Also check out the Least Common Multiple of 17700 and 17710