What is the Greatest Common Factor of 32688 and 32704?

Greatest common factor (GCF) of 32688 and 32704 is 16.

GCF(32688,32704) = 16

We will now calculate the prime factors of 32688 and 32704, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 32688 and 32704.

How to find the GCF of 32688 and 32704?

We will first find the prime factorization of 32688 and 32704. After we will calculate the factors of 32688 and 32704 and find the biggest common factor number .

Step-1: Prime Factorization of 32688

Prime factors of 32688 are 2, 3, 227. Prime factorization of 32688 in exponential form is:

32688 = 2⁴ × 3² × 227¹

Step-2: 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-3: Factors of 32688

List of positive integer factors of 32688 that divides 32688 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144, 227, 454, 681, 908, 1362, 1816, 2043, 2724, 3632, 4086, 5448, 8172, 10896, 16344

Step-4: Factors of 32704

List of positive integer factors of 32704 that divides 32688 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 32688 and 32704. The biggest common factor number is the GCF number.
So the greatest common factor 32688 and 32704 is 16.

Also check out the Least Common Multiple of 32688 and 32704