What is the Greatest Common Factor of 49488 and 49500?

Greatest common factor (GCF) of 49488 and 49500 is 12.

GCF(49488,49500) = 12

We will now calculate the prime factors of 49488 and 49500, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 49488 and 49500.

How to find the GCF of 49488 and 49500?

We will first find the prime factorization of 49488 and 49500. After we will calculate the factors of 49488 and 49500 and find the biggest common factor number .

Step-1: Prime Factorization of 49488

Prime factors of 49488 are 2, 3, 1031. Prime factorization of 49488 in exponential form is:

49488 = 2⁴ × 3¹ × 1031¹

Step-2: Prime Factorization of 49500

Prime factors of 49500 are 2, 3, 5, 11. Prime factorization of 49500 in exponential form is:

49500 = 2² × 3² × 5³ × 11¹

Step-3: Factors of 49488

List of positive integer factors of 49488 that divides 49488 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 1031, 2062, 3093, 4124, 6186, 8248, 12372, 16496, 24744

Step-4: Factors of 49500

List of positive integer factors of 49500 that divides 49488 without a remainder.

1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 25, 30, 33, 36, 44, 45, 50, 55, 60, 66, 75, 90, 99, 100, 110, 125, 132, 150, 165, 180, 198, 220, 225, 250, 275, 300, 330, 375, 396, 450, 495, 500, 550, 660, 750, 825, 900, 990, 1100, 1125, 1375, 1500, 1650, 1980, 2250, 2475, 2750, 3300, 4125, 4500, 4950, 5500, 8250, 9900, 12375, 16500, 24750

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 49488 and 49500. The biggest common factor number is the GCF number.
So the greatest common factor 49488 and 49500 is 12.

Also check out the Least Common Multiple of 49488 and 49500