What is the Greatest Common Factor of 24705 and 24714?

Greatest common factor (GCF) of 24705 and 24714 is 9.

GCF(24705,24714) = 9

We will now calculate the prime factors of 24705 and 24714, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 24705 and 24714.

How to find the GCF of 24705 and 24714?

We will first find the prime factorization of 24705 and 24714. After we will calculate the factors of 24705 and 24714 and find the biggest common factor number .

Step-1: Prime Factorization of 24705

Prime factors of 24705 are 3, 5, 61. Prime factorization of 24705 in exponential form is:

24705 = 3⁴ × 5¹ × 61¹

Step-2: Prime Factorization of 24714

Prime factors of 24714 are 2, 3, 1373. Prime factorization of 24714 in exponential form is:

24714 = 2¹ × 3² × 1373¹

Step-3: Factors of 24705

List of positive integer factors of 24705 that divides 24705 without a remainder.

1, 3, 5, 9, 15, 27, 45, 61, 81, 135, 183, 305, 405, 549, 915, 1647, 2745, 4941, 8235

Step-4: Factors of 24714

List of positive integer factors of 24714 that divides 24705 without a remainder.

1, 2, 3, 6, 9, 18, 1373, 2746, 4119, 8238, 12357

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 24705 and 24714. The biggest common factor number is the GCF number.
So the greatest common factor 24705 and 24714 is 9.

Also check out the Least Common Multiple of 24705 and 24714