What is the Greatest Common Factor of 14097 and 14112?

Greatest common factor (GCF) of 14097 and 14112 is 3.

GCF(14097,14112) = 3

We will now calculate the prime factors of 14097 and 14112, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14097 and 14112.

How to find the GCF of 14097 and 14112?

We will first find the prime factorization of 14097 and 14112. After we will calculate the factors of 14097 and 14112 and find the biggest common factor number .

Step-1: Prime Factorization of 14097

Prime factors of 14097 are 3, 37, 127. Prime factorization of 14097 in exponential form is:

14097 = 3¹ × 37¹ × 127¹

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 14097

List of positive integer factors of 14097 that divides 14097 without a remainder.

1, 3, 37, 111, 127, 381, 4699

Step-4: Factors of 14112

List of positive integer factors of 14112 that divides 14097 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 14097 and 14112. The biggest common factor number is the GCF number.
So the greatest common factor 14097 and 14112 is 3.

Also check out the Least Common Multiple of 14097 and 14112