What is the Greatest Common Factor of 9690 and 9705?

Greatest common factor (GCF) of 9690 and 9705 is 15.

GCF(9690,9705) = 15

We will now calculate the prime factors of 9690 and 9705, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 9690 and 9705.

How to find the GCF of 9690 and 9705?

We will first find the prime factorization of 9690 and 9705. After we will calculate the factors of 9690 and 9705 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 9705

Prime factors of 9705 are 3, 5, 647. Prime factorization of 9705 in exponential form is:

9705 = 3¹ × 5¹ × 647¹

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 9705

List of positive integer factors of 9705 that divides 9690 without a remainder.

1, 3, 5, 15, 647, 1941, 3235

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 9690 and 9705. The biggest common factor number is the GCF number.
So the greatest common factor 9690 and 9705 is 15.

Also check out the Least Common Multiple of 9690 and 9705