What is the Greatest Common Factor of 32700 and 32704?

Greatest common factor (GCF) of 32700 and 32704 is 4.

GCF(32700,32704) = 4

We will now calculate the prime factors of 32700 and 32704, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 32700 and 32704.

How to find the GCF of 32700 and 32704?

We will first find the prime factorization of 32700 and 32704. After we will calculate the factors of 32700 and 32704 and find the biggest common factor number .

Step-1: Prime Factorization of 32700

Prime factors of 32700 are 2, 3, 5, 109. Prime factorization of 32700 in exponential form is:

32700 = 2² × 3¹ × 5² × 109¹

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 32700

List of positive integer factors of 32700 that divides 32700 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 109, 150, 218, 300, 327, 436, 545, 654, 1090, 1308, 1635, 2180, 2725, 3270, 5450, 6540, 8175, 10900, 16350

Step-4: Factors of 32704

List of positive integer factors of 32704 that divides 32700 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 32700 and 32704. The biggest common factor number is the GCF number.
So the greatest common factor 32700 and 32704 is 4.

Also check out the Least Common Multiple of 32700 and 32704