What is the Greatest Common Factor of 49800 and 49814?

Greatest common factor (GCF) of 49800 and 49814 is 2.

GCF(49800,49814) = 2

We will now calculate the prime factors of 49800 and 49814, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 49800 and 49814.

How to find the GCF of 49800 and 49814?

We will first find the prime factorization of 49800 and 49814. After we will calculate the factors of 49800 and 49814 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 49814

Prime factors of 49814 are 2, 24907. Prime factorization of 49814 in exponential form is:

49814 = 2¹ × 24907¹

Step-3: Factors of 49800

List of positive integer factors of 49800 that divides 49800 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

Step-4: Factors of 49814

List of positive integer factors of 49814 that divides 49800 without a remainder.

1, 2, 24907

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 49800 and 49814. The biggest common factor number is the GCF number.
So the greatest common factor 49800 and 49814 is 2.

Also check out the Least Common Multiple of 49800 and 49814