What is the Greatest Common Factor of 1400 and 1414?

Greatest common factor (GCF) of 1400 and 1414 is 14.

GCF(1400,1414) = 14

We will now calculate the prime factors of 1400 and 1414, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1400 and 1414.

How to find the GCF of 1400 and 1414?

We will first find the prime factorization of 1400 and 1414. After we will calculate the factors of 1400 and 1414 and find the biggest common factor number .

Step-1: Prime Factorization of 1400

Prime factors of 1400 are 2, 5, 7. Prime factorization of 1400 in exponential form is:

1400 = 2³ × 5² × 7¹

Step-2: 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-3: Factors of 1400

List of positive integer factors of 1400 that divides 1400 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 50, 56, 70, 100, 140, 175, 200, 280, 350, 700

Step-4: Factors of 1414

List of positive integer factors of 1414 that divides 1400 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1400 and 1414. The biggest common factor number is the GCF number.
So the greatest common factor 1400 and 1414 is 14.

Also check out the Least Common Multiple of 1400 and 1414