What is the Greatest Common Factor of 32704 and 32724?

Greatest common factor (GCF) of 32704 and 32724 is 4.

GCF(32704,32724) = 4

We will now calculate the prime factors of 32704 and 32724, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 32704 and 32724.

How to find the GCF of 32704 and 32724?

We will first find the prime factorization of 32704 and 32724. After we will calculate the factors of 32704 and 32724 and find the biggest common factor number .

Step-1: Prime Factorization of 32704

Prime factors of 32704 are 2, 7, 73. Prime factorization of 32704 in exponential form is:

32704 = 2⁶ × 7¹ × 73¹

Step-2: 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-3: Factors of 32704

List of positive integer factors of 32704 that divides 32704 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 73, 112, 146, 224, 292, 448, 511, 584, 1022, 1168, 2044, 2336, 4088, 4672, 8176, 16352

Step-4: Factors of 32724

List of positive integer factors of 32724 that divides 32704 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 32704 and 32724. The biggest common factor number is the GCF number.
So the greatest common factor 32704 and 32724 is 4.

Also check out the Least Common Multiple of 32704 and 32724