What is the Greatest Common Factor of 14 and 182?

Greatest common factor (GCF) of 14 and 182 is 14.

GCF(14,182) = 14

We will now calculate the prime factors of 14 and 182, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14 and 182.

How to find the GCF of 14 and 182?

We will first find the prime factorization of 14 and 182. After we will calculate the factors of 14 and 182 and find the biggest common factor number .

Step-1: Prime Factorization of 14

Prime factors of 14 are 2, 7. Prime factorization of 14 in exponential form is:

14 = 2¹ × 7¹

Step-2: Prime Factorization of 182

Prime factors of 182 are 2, 7, 13. Prime factorization of 182 in exponential form is:

182 = 2¹ × 7¹ × 13¹

Step-3: Factors of 14

List of positive integer factors of 14 that divides 14 without a remainder.

1, 2, 7

Step-4: Factors of 182

List of positive integer factors of 182 that divides 14 without a remainder.

1, 2, 7, 13, 14, 26, 91

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14 and 182. The biggest common factor number is the GCF number.
So the greatest common factor 14 and 182 is 14.

Also check out the Least Common Multiple of 14 and 182