What is the Greatest Common Factor of 49500 and 49509?

Greatest common factor (GCF) of 49500 and 49509 is 9.

GCF(49500,49509) = 9

We will now calculate the prime factors of 49500 and 49509, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 49500 and 49509.

How to find the GCF of 49500 and 49509?

We will first find the prime factorization of 49500 and 49509. After we will calculate the factors of 49500 and 49509 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 49509

Prime factors of 49509 are 3, 5501. Prime factorization of 49509 in exponential form is:

49509 = 3² × 5501¹

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 49509

List of positive integer factors of 49509 that divides 49500 without a remainder.

1, 3, 9, 5501, 16503

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 49500 and 49509. The biggest common factor number is the GCF number.
So the greatest common factor 49500 and 49509 is 9.

Also check out the Least Common Multiple of 49500 and 49509