What is the Greatest Common Factor of 9688 and 9705?

Greatest common factor (GCF) of 9688 and 9705 is 1.

GCF(9688,9705) = 1

We will now calculate the prime factors of 9688 and 9705, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 9688 and 9705.

How to find the GCF of 9688 and 9705?

We will first find the prime factorization of 9688 and 9705. After we will calculate the factors of 9688 and 9705 and find the biggest common factor number .

Step-1: Prime Factorization of 9688

Prime factors of 9688 are 2, 7, 173. Prime factorization of 9688 in exponential form is:

9688 = 2³ × 7¹ × 173¹

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 9688

List of positive integer factors of 9688 that divides 9688 without a remainder.

1, 2, 4, 7, 8, 14, 28, 56, 173, 346, 692, 1211, 1384, 2422, 4844

Step-4: Factors of 9705

List of positive integer factors of 9705 that divides 9688 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 9688 and 9705. The biggest common factor number is the GCF number.
So the greatest common factor 9688 and 9705 is 1.

Also check out the Least Common Multiple of 9688 and 9705