What is the Greatest Common Factor of 9696 and 9705?

Greatest common factor (GCF) of 9696 and 9705 is 3.

GCF(9696,9705) = 3

We will now calculate the prime factors of 9696 and 9705, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 9696 and 9705.

How to find the GCF of 9696 and 9705?

We will first find the prime factorization of 9696 and 9705. After we will calculate the factors of 9696 and 9705 and find the biggest common factor number .

Step-1: Prime Factorization of 9696

Prime factors of 9696 are 2, 3, 101. Prime factorization of 9696 in exponential form is:

9696 = 2⁵ × 3¹ × 101¹

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 9696

List of positive integer factors of 9696 that divides 9696 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96, 101, 202, 303, 404, 606, 808, 1212, 1616, 2424, 3232, 4848

Step-4: Factors of 9705

List of positive integer factors of 9705 that divides 9696 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 9696 and 9705. The biggest common factor number is the GCF number.
So the greatest common factor 9696 and 9705 is 3.

Also check out the Least Common Multiple of 9696 and 9705