What is the Greatest Common Factor of 13706 and 13725?

Greatest common factor (GCF) of 13706 and 13725 is 1.

GCF(13706,13725) = 1

We will now calculate the prime factors of 13706 and 13725, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13706 and 13725.

How to find the GCF of 13706 and 13725?

We will first find the prime factorization of 13706 and 13725. After we will calculate the factors of 13706 and 13725 and find the biggest common factor number .

Step-1: Prime Factorization of 13706

Prime factors of 13706 are 2, 7, 11, 89. Prime factorization of 13706 in exponential form is:

13706 = 2¹ × 7¹ × 11¹ × 89¹

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 13706

List of positive integer factors of 13706 that divides 13706 without a remainder.

1, 2, 7, 11, 14, 22, 77, 89, 154, 178, 623, 979, 1246, 1958, 6853

Step-4: Factors of 13725

List of positive integer factors of 13725 that divides 13706 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 13706 and 13725. The biggest common factor number is the GCF number.
So the greatest common factor 13706 and 13725 is 1.

Also check out the Least Common Multiple of 13706 and 13725