What is the Greatest Common Factor of 14 and 140?

Greatest common factor (GCF) of 14 and 140 is 14.

GCF(14,140) = 14

We will now calculate the prime factors of 14 and 140, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14 and 140.

How to find the GCF of 14 and 140?

We will first find the prime factorization of 14 and 140. After we will calculate the factors of 14 and 140 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 140

Prime factors of 140 are 2, 5, 7. Prime factorization of 140 in exponential form is:

140 = 2² × 5¹ × 7¹

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 140

List of positive integer factors of 140 that divides 14 without a remainder.

1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14 and 140. The biggest common factor number is the GCF number.
So the greatest common factor 14 and 140 is 14.

Also check out the Least Common Multiple of 14 and 140