What is the Greatest Common Factor of 10690 and 10710?

Greatest common factor (GCF) of 10690 and 10710 is 10.

GCF(10690,10710) = 10

We will now calculate the prime factors of 10690 and 10710, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10690 and 10710.

How to find the GCF of 10690 and 10710?

We will first find the prime factorization of 10690 and 10710. After we will calculate the factors of 10690 and 10710 and find the biggest common factor number .

Step-1: Prime Factorization of 10690

Prime factors of 10690 are 2, 5, 1069. Prime factorization of 10690 in exponential form is:

10690 = 2¹ × 5¹ × 1069¹

Step-2: Prime Factorization of 10710

Prime factors of 10710 are 2, 3, 5, 7, 17. Prime factorization of 10710 in exponential form is:

10710 = 2¹ × 3² × 5¹ × 7¹ × 17¹

Step-3: Factors of 10690

List of positive integer factors of 10690 that divides 10690 without a remainder.

1, 2, 5, 10, 1069, 2138, 5345

Step-4: Factors of 10710

List of positive integer factors of 10710 that divides 10690 without a remainder.

1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 17, 18, 21, 30, 34, 35, 42, 45, 51, 63, 70, 85, 90, 102, 105, 119, 126, 153, 170, 210, 238, 255, 306, 315, 357, 510, 595, 630, 714, 765, 1071, 1190, 1530, 1785, 2142, 3570, 5355

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10690 and 10710. The biggest common factor number is the GCF number.
So the greatest common factor 10690 and 10710 is 10.

Also check out the Least Common Multiple of 10690 and 10710