What is the Greatest Common Factor of 49584 and 49590?

Greatest common factor (GCF) of 49584 and 49590 is 6.

GCF(49584,49590) = 6

We will now calculate the prime factors of 49584 and 49590, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 49584 and 49590.

How to find the GCF of 49584 and 49590?

We will first find the prime factorization of 49584 and 49590. After we will calculate the factors of 49584 and 49590 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 49590

Prime factors of 49590 are 2, 3, 5, 19, 29. Prime factorization of 49590 in exponential form is:

49590 = 2¹ × 3² × 5¹ × 19¹ × 29¹

Step-3: Factors of 49584

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

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

Step-4: Factors of 49590

List of positive integer factors of 49590 that divides 49584 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 19, 29, 30, 38, 45, 57, 58, 87, 90, 95, 114, 145, 171, 174, 190, 261, 285, 290, 342, 435, 522, 551, 570, 855, 870, 1102, 1305, 1653, 1710, 2610, 2755, 3306, 4959, 5510, 8265, 9918, 16530, 24795

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 49584 and 49590. The biggest common factor number is the GCF number.
So the greatest common factor 49584 and 49590 is 6.

Also check out the Least Common Multiple of 49584 and 49590