What is the Greatest Common Factor of 1400 and 1409?

Greatest common factor (GCF) of 1400 and 1409 is 1.

GCF(1400,1409) = 1

We will now calculate the prime factors of 1400 and 1409, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1400 and 1409.

How to find the GCF of 1400 and 1409?

We will first find the prime factorization of 1400 and 1409. After we will calculate the factors of 1400 and 1409 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 1409

Prime factors of 1409 are 1409. Prime factorization of 1409 in exponential form is:

1409 = 1409¹

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 1409

List of positive integer factors of 1409 that divides 1400 without a remainder.

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1400 and 1409. The biggest common factor number is the GCF number.
So the greatest common factor 1400 and 1409 is 1.

Also check out the Least Common Multiple of 1400 and 1409