What is the Greatest Common Factor of 13734 and 13752?

Greatest common factor (GCF) of 13734 and 13752 is 18.

GCF(13734,13752) = 18

We will now calculate the prime factors of 13734 and 13752, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 13734 and 13752.

How to find the GCF of 13734 and 13752?

We will first find the prime factorization of 13734 and 13752. After we will calculate the factors of 13734 and 13752 and find the biggest common factor number .

Step-1: Prime Factorization of 13734

Prime factors of 13734 are 2, 3, 7, 109. Prime factorization of 13734 in exponential form is:

13734 = 2¹ × 3² × 7¹ × 109¹

Step-2: Prime Factorization of 13752

Prime factors of 13752 are 2, 3, 191. Prime factorization of 13752 in exponential form is:

13752 = 2³ × 3² × 191¹

Step-3: Factors of 13734

List of positive integer factors of 13734 that divides 13734 without a remainder.

1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 109, 126, 218, 327, 654, 763, 981, 1526, 1962, 2289, 4578, 6867

Step-4: Factors of 13752

List of positive integer factors of 13752 that divides 13734 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72, 191, 382, 573, 764, 1146, 1528, 1719, 2292, 3438, 4584, 6876

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 13734 and 13752. The biggest common factor number is the GCF number.
So the greatest common factor 13734 and 13752 is 18.

Also check out the Least Common Multiple of 13734 and 13752