What is the Greatest Common Factor of 32724 and 32742?

Greatest common factor (GCF) of 32724 and 32742 is 18.

GCF(32724,32742) = 18

We will now calculate the prime factors of 32724 and 32742, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 32724 and 32742.

How to find the GCF of 32724 and 32742?

We will first find the prime factorization of 32724 and 32742. After we will calculate the factors of 32724 and 32742 and find the biggest common factor number .

Step-1: Prime Factorization of 32724

Prime factors of 32724 are 2, 3, 101. Prime factorization of 32724 in exponential form is:

32724 = 2² × 3⁴ × 101¹

Step-2: Prime Factorization of 32742

Prime factors of 32742 are 2, 3, 17, 107. Prime factorization of 32742 in exponential form is:

32742 = 2¹ × 3² × 17¹ × 107¹

Step-3: Factors of 32724

List of positive integer factors of 32724 that divides 32724 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 101, 108, 162, 202, 303, 324, 404, 606, 909, 1212, 1818, 2727, 3636, 5454, 8181, 10908, 16362

Step-4: Factors of 32742

List of positive integer factors of 32742 that divides 32724 without a remainder.

1, 2, 3, 6, 9, 17, 18, 34, 51, 102, 107, 153, 214, 306, 321, 642, 963, 1819, 1926, 3638, 5457, 10914, 16371

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 32724 and 32742. The biggest common factor number is the GCF number.
So the greatest common factor 32724 and 32742 is 18.

Also check out the Least Common Multiple of 32724 and 32742