What is the Greatest Common Factor of 1414 and 1430?

Greatest common factor (GCF) of 1414 and 1430 is 2.

GCF(1414,1430) = 2

We will now calculate the prime factors of 1414 and 1430, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1414 and 1430.

How to find the GCF of 1414 and 1430?

We will first find the prime factorization of 1414 and 1430. After we will calculate the factors of 1414 and 1430 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 1430

Prime factors of 1430 are 2, 5, 11, 13. Prime factorization of 1430 in exponential form is:

1430 = 2¹ × 5¹ × 11¹ × 13¹

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 1430

List of positive integer factors of 1430 that divides 1414 without a remainder.

1, 2, 5, 10, 11, 13, 22, 26, 55, 65, 110, 130, 143, 286, 715

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1414 and 1430. The biggest common factor number is the GCF number.
So the greatest common factor 1414 and 1430 is 2.

Also check out the Least Common Multiple of 1414 and 1430