What is the Greatest Common Factor of 44100 and 44116?

Greatest common factor (GCF) of 44100 and 44116 is 4.

GCF(44100,44116) = 4

We will now calculate the prime factors of 44100 and 44116, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 44100 and 44116.

How to find the GCF of 44100 and 44116?

We will first find the prime factorization of 44100 and 44116. After we will calculate the factors of 44100 and 44116 and find the biggest common factor number .

Step-1: Prime Factorization of 44100

Prime factors of 44100 are 2, 3, 5, 7. Prime factorization of 44100 in exponential form is:

44100 = 2² × 3² × 5² × 7²

Step-2: Prime Factorization of 44116

Prime factors of 44116 are 2, 41, 269. Prime factorization of 44116 in exponential form is:

44116 = 2² × 41¹ × 269¹

Step-3: Factors of 44100

List of positive integer factors of 44100 that divides 44100 without a remainder.

1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 25, 28, 30, 35, 36, 42, 45, 49, 50, 60, 63, 70, 75, 84, 90, 98, 100, 105, 126, 140, 147, 150, 175, 180, 196, 210, 225, 245, 252, 294, 300, 315, 350, 420, 441, 450, 490, 525, 588, 630, 700, 735, 882, 900, 980, 1050, 1225, 1260, 1470, 1575, 1764, 2100, 2205, 2450, 2940, 3150, 3675, 4410, 4900, 6300, 7350, 8820, 11025, 14700, 22050

Step-4: Factors of 44116

List of positive integer factors of 44116 that divides 44100 without a remainder.

1, 2, 4, 41, 82, 164, 269, 538, 1076, 11029, 22058

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 44100 and 44116. The biggest common factor number is the GCF number.
So the greatest common factor 44100 and 44116 is 4.

Also check out the Least Common Multiple of 44100 and 44116