What is the Greatest Common Factor of 49500 and 49512?

Greatest common factor (GCF) of 49500 and 49512 is 12.

GCF(49500,49512) = 12

We will now calculate the prime factors of 49500 and 49512, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 49500 and 49512.

How to find the GCF of 49500 and 49512?

We will first find the prime factorization of 49500 and 49512. After we will calculate the factors of 49500 and 49512 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 49512

Prime factors of 49512 are 2, 3, 2063. Prime factorization of 49512 in exponential form is:

49512 = 2³ × 3¹ × 2063¹

Step-3: Factors of 49500

List of positive integer factors of 49500 that divides 49500 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

Step-4: Factors of 49512

List of positive integer factors of 49512 that divides 49500 without a remainder.

1, 2, 3, 4, 6, 8, 12, 24, 2063, 4126, 6189, 8252, 12378, 16504, 24756

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 49500 and 49512. The biggest common factor number is the GCF number.
So the greatest common factor 49500 and 49512 is 12.

Also check out the Least Common Multiple of 49500 and 49512