What is the Greatest Common Factor of 73575 and 73584?

Greatest common factor (GCF) of 73575 and 73584 is 9.

GCF(73575,73584) = 9

We will now calculate the prime factors of 73575 and 73584, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 73575 and 73584.

How to find the GCF of 73575 and 73584?

We will first find the prime factorization of 73575 and 73584. After we will calculate the factors of 73575 and 73584 and find the biggest common factor number .

Step-1: Prime Factorization of 73575

Prime factors of 73575 are 3, 5, 109. Prime factorization of 73575 in exponential form is:

73575 = 3³ × 5² × 109¹

Step-2: Prime Factorization of 73584

Prime factors of 73584 are 2, 3, 7, 73. Prime factorization of 73584 in exponential form is:

73584 = 2⁴ × 3² × 7¹ × 73¹

Step-3: Factors of 73575

List of positive integer factors of 73575 that divides 73575 without a remainder.

1, 3, 5, 9, 15, 25, 27, 45, 75, 109, 135, 225, 327, 545, 675, 981, 1635, 2725, 2943, 4905, 8175, 14715, 24525

Step-4: Factors of 73584

List of positive integer factors of 73584 that divides 73575 without a remainder.

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 36, 42, 48, 56, 63, 72, 73, 84, 112, 126, 144, 146, 168, 219, 252, 292, 336, 438, 504, 511, 584, 657, 876, 1008, 1022, 1168, 1314, 1533, 1752, 2044, 2628, 3066, 3504, 4088, 4599, 5256, 6132, 8176, 9198, 10512, 12264, 18396, 24528, 36792

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 73575 and 73584. The biggest common factor number is the GCF number.
So the greatest common factor 73575 and 73584 is 9.

Also check out the Least Common Multiple of 73575 and 73584