What is the Greatest Common Factor of 1414 and 1421?

Greatest common factor (GCF) of 1414 and 1421 is 7.

GCF(1414,1421) = 7

We will now calculate the prime factors of 1414 and 1421, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1414 and 1421.

How to find the GCF of 1414 and 1421?

We will first find the prime factorization of 1414 and 1421. After we will calculate the factors of 1414 and 1421 and find the biggest common factor number .

Step-1: Prime Factorization of 1414

Prime factors of 1414 are 2, 7, 101. Prime factorization of 1414 in exponential form is:

1414 = 2¹ × 7¹ × 101¹

Step-2: Prime Factorization of 1421

Prime factors of 1421 are 7, 29. Prime factorization of 1421 in exponential form is:

1421 = 7² × 29¹

Step-3: Factors of 1414

List of positive integer factors of 1414 that divides 1414 without a remainder.

1, 2, 7, 14, 101, 202, 707

Step-4: Factors of 1421

List of positive integer factors of 1421 that divides 1414 without a remainder.

1, 7, 29, 49, 203

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1414 and 1421. The biggest common factor number is the GCF number.
So the greatest common factor 1414 and 1421 is 7.

Also check out the Least Common Multiple of 1414 and 1421