What is the Greatest Common Factor of 14105 and 14112?

Greatest common factor (GCF) of 14105 and 14112 is 7.

GCF(14105,14112) = 7

We will now calculate the prime factors of 14105 and 14112, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14105 and 14112.

How to find the GCF of 14105 and 14112?

We will first find the prime factorization of 14105 and 14112. After we will calculate the factors of 14105 and 14112 and find the biggest common factor number .

Step-1: Prime Factorization of 14105

Prime factors of 14105 are 5, 7, 13, 31. Prime factorization of 14105 in exponential form is:

14105 = 5¹ × 7¹ × 13¹ × 31¹

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 14105

List of positive integer factors of 14105 that divides 14105 without a remainder.

1, 5, 7, 13, 31, 35, 65, 91, 155, 217, 403, 455, 1085, 2015, 2821

Step-4: Factors of 14112

List of positive integer factors of 14112 that divides 14105 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 14105 and 14112. The biggest common factor number is the GCF number.
So the greatest common factor 14105 and 14112 is 7.

Also check out the Least Common Multiple of 14105 and 14112