What is the Greatest Common Factor of 49785 and 49800?

Greatest common factor (GCF) of 49785 and 49800 is 15.

GCF(49785,49800) = 15

We will now calculate the prime factors of 49785 and 49800, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 49785 and 49800.

How to find the GCF of 49785 and 49800?

We will first find the prime factorization of 49785 and 49800. After we will calculate the factors of 49785 and 49800 and find the biggest common factor number .

Step-1: Prime Factorization of 49785

Prime factors of 49785 are 3, 5, 3319. Prime factorization of 49785 in exponential form is:

49785 = 3¹ × 5¹ × 3319¹

Step-2: Prime Factorization of 49800

Prime factors of 49800 are 2, 3, 5, 83. Prime factorization of 49800 in exponential form is:

49800 = 2³ × 3¹ × 5² × 83¹

Step-3: Factors of 49785

List of positive integer factors of 49785 that divides 49785 without a remainder.

1, 3, 5, 15, 3319, 9957, 16595

Step-4: Factors of 49800

List of positive integer factors of 49800 that divides 49785 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 83, 100, 120, 150, 166, 200, 249, 300, 332, 415, 498, 600, 664, 830, 996, 1245, 1660, 1992, 2075, 2490, 3320, 4150, 4980, 6225, 8300, 9960, 12450, 16600, 24900

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 49785 and 49800. The biggest common factor number is the GCF number.
So the greatest common factor 49785 and 49800 is 15.

Also check out the Least Common Multiple of 49785 and 49800