What is the Greatest Common Factor of 9705 and 9714?

Greatest common factor (GCF) of 9705 and 9714 is 3.

GCF(9705,9714) = 3

We will now calculate the prime factors of 9705 and 9714, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 9705 and 9714.

How to find the GCF of 9705 and 9714?

We will first find the prime factorization of 9705 and 9714. After we will calculate the factors of 9705 and 9714 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 9714

Prime factors of 9714 are 2, 3, 1619. Prime factorization of 9714 in exponential form is:

9714 = 2¹ × 3¹ × 1619¹

Step-3: Factors of 9705

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

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

Step-4: Factors of 9714

List of positive integer factors of 9714 that divides 9705 without a remainder.

1, 2, 3, 6, 1619, 3238, 4857

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 9705 and 9714. The biggest common factor number is the GCF number.
So the greatest common factor 9705 and 9714 is 3.

Also check out the Least Common Multiple of 9705 and 9714