What is the Greatest Common Factor of 9690 and 9710?

Greatest common factor (GCF) of 9690 and 9710 is 10.

GCF(9690,9710) = 10

We will now calculate the prime factors of 9690 and 9710, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 9690 and 9710.

How to find the GCF of 9690 and 9710?

We will first find the prime factorization of 9690 and 9710. After we will calculate the factors of 9690 and 9710 and find the biggest common factor number .

Step-1: Prime Factorization of 9690

Prime factors of 9690 are 2, 3, 5, 17, 19. Prime factorization of 9690 in exponential form is:

9690 = 2¹ × 3¹ × 5¹ × 17¹ × 19¹

Step-2: Prime Factorization of 9710

Prime factors of 9710 are 2, 5, 971. Prime factorization of 9710 in exponential form is:

9710 = 2¹ × 5¹ × 971¹

Step-3: Factors of 9690

List of positive integer factors of 9690 that divides 9690 without a remainder.

1, 2, 3, 5, 6, 10, 15, 17, 19, 30, 34, 38, 51, 57, 85, 95, 102, 114, 170, 190, 255, 285, 323, 510, 570, 646, 969, 1615, 1938, 3230, 4845

Step-4: Factors of 9710

List of positive integer factors of 9710 that divides 9690 without a remainder.

1, 2, 5, 10, 971, 1942, 4855

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 9690 and 9710. The biggest common factor number is the GCF number.
So the greatest common factor 9690 and 9710 is 10.

Also check out the Least Common Multiple of 9690 and 9710