What is the Greatest Common Factor of 9705 and 9720?

Greatest common factor (GCF) of 9705 and 9720 is 15.

GCF(9705,9720) = 15

We will now calculate the prime factors of 9705 and 9720, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 9705 and 9720.

How to find the GCF of 9705 and 9720?

We will first find the prime factorization of 9705 and 9720. After we will calculate the factors of 9705 and 9720 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 9720

Prime factors of 9720 are 2, 3, 5. Prime factorization of 9720 in exponential form is:

9720 = 2³ × 3⁵ × 5¹

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 9720

List of positive integer factors of 9720 that divides 9705 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 30, 36, 40, 45, 54, 60, 72, 81, 90, 108, 120, 135, 162, 180, 216, 243, 270, 324, 360, 405, 486, 540, 648, 810, 972, 1080, 1215, 1620, 1944, 2430, 3240, 4860

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 9705 and 9720. The biggest common factor number is the GCF number.
So the greatest common factor 9705 and 9720 is 15.

Also check out the Least Common Multiple of 9705 and 9720