What is the Greatest Common Factor of 14100 and 14112?

Greatest common factor (GCF) of 14100 and 14112 is 12.

GCF(14100,14112) = 12

We will now calculate the prime factors of 14100 and 14112, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14100 and 14112.

How to find the GCF of 14100 and 14112?

We will first find the prime factorization of 14100 and 14112. After we will calculate the factors of 14100 and 14112 and find the biggest common factor number .

Step-1: Prime Factorization of 14100

Prime factors of 14100 are 2, 3, 5, 47. Prime factorization of 14100 in exponential form is:

14100 = 2² × 3¹ × 5² × 47¹

Step-2: Prime Factorization of 14112

Prime factors of 14112 are 2, 3, 7. Prime factorization of 14112 in exponential form is:

14112 = 2⁵ × 3² × 7²

Step-3: Factors of 14100

List of positive integer factors of 14100 that divides 14100 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 47, 50, 60, 75, 94, 100, 141, 150, 188, 235, 282, 300, 470, 564, 705, 940, 1175, 1410, 2350, 2820, 3525, 4700, 7050

Step-4: Factors of 14112

List of positive integer factors of 14112 that divides 14100 without a remainder.

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 32, 36, 42, 48, 49, 56, 63, 72, 84, 96, 98, 112, 126, 144, 147, 168, 196, 224, 252, 288, 294, 336, 392, 441, 504, 588, 672, 784, 882, 1008, 1176, 1568, 1764, 2016, 2352, 3528, 4704, 7056

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14100 and 14112. The biggest common factor number is the GCF number.
So the greatest common factor 14100 and 14112 is 12.

Also check out the Least Common Multiple of 14100 and 14112