What is the Greatest Common Factor of 49500 and 49514?

Greatest common factor (GCF) of 49500 and 49514 is 2.

GCF(49500,49514) = 2

We will now calculate the prime factors of 49500 and 49514, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 49500 and 49514.

How to find the GCF of 49500 and 49514?

We will first find the prime factorization of 49500 and 49514. After we will calculate the factors of 49500 and 49514 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 49514

Prime factors of 49514 are 2, 19, 1303. Prime factorization of 49514 in exponential form is:

49514 = 2¹ × 19¹ × 1303¹

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 49514

List of positive integer factors of 49514 that divides 49500 without a remainder.

1, 2, 19, 38, 1303, 2606, 24757

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 49500 and 49514. The biggest common factor number is the GCF number.
So the greatest common factor 49500 and 49514 is 2.

Also check out the Least Common Multiple of 49500 and 49514