What is the Greatest Common Factor of 49575 and 49584?

Greatest common factor (GCF) of 49575 and 49584 is 3.

GCF(49575,49584) = 3

We will now calculate the prime factors of 49575 and 49584, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 49575 and 49584.

How to find the GCF of 49575 and 49584?

We will first find the prime factorization of 49575 and 49584. After we will calculate the factors of 49575 and 49584 and find the biggest common factor number .

Step-1: Prime Factorization of 49575

Prime factors of 49575 are 3, 5, 661. Prime factorization of 49575 in exponential form is:

49575 = 3¹ × 5² × 661¹

Step-2: Prime Factorization of 49584

Prime factors of 49584 are 2, 3, 1033. Prime factorization of 49584 in exponential form is:

49584 = 2⁴ × 3¹ × 1033¹

Step-3: Factors of 49575

List of positive integer factors of 49575 that divides 49575 without a remainder.

1, 3, 5, 15, 25, 75, 661, 1983, 3305, 9915, 16525

Step-4: Factors of 49584

List of positive integer factors of 49584 that divides 49575 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 1033, 2066, 3099, 4132, 6198, 8264, 12396, 16528, 24792

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 49575 and 49584. The biggest common factor number is the GCF number.
So the greatest common factor 49575 and 49584 is 3.

Also check out the Least Common Multiple of 49575 and 49584