What is the Greatest Common Factor of 13705 and 13725?

Greatest common factor (GCF) of 13705 and 13725 is 5.

GCF(13705,13725) = 5

We will now calculate the prime factors of 13705 and 13725, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13705 and 13725.

How to find the GCF of 13705 and 13725?

We will first find the prime factorization of 13705 and 13725. After we will calculate the factors of 13705 and 13725 and find the biggest common factor number .

Step-1: Prime Factorization of 13705

Prime factors of 13705 are 5, 2741. Prime factorization of 13705 in exponential form is:

13705 = 5¹ × 2741¹

Step-2: Prime Factorization of 13725

Prime factors of 13725 are 3, 5, 61. Prime factorization of 13725 in exponential form is:

13725 = 3² × 5² × 61¹

Step-3: Factors of 13705

List of positive integer factors of 13705 that divides 13705 without a remainder.

1, 5, 2741

Step-4: Factors of 13725

List of positive integer factors of 13725 that divides 13705 without a remainder.

1, 3, 5, 9, 15, 25, 45, 61, 75, 183, 225, 305, 549, 915, 1525, 2745, 4575

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13705 and 13725. The biggest common factor number is the GCF number.
So the greatest common factor 13705 and 13725 is 5.

Also check out the Least Common Multiple of 13705 and 13725