What is the Greatest Common Factor of 1400 and 1419?

Greatest common factor (GCF) of 1400 and 1419 is 1.

GCF(1400,1419) = 1

We will now calculate the prime factors of 1400 and 1419, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1400 and 1419.

How to find the GCF of 1400 and 1419?

We will first find the prime factorization of 1400 and 1419. After we will calculate the factors of 1400 and 1419 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 1419

Prime factors of 1419 are 3, 11, 43. Prime factorization of 1419 in exponential form is:

1419 = 3¹ × 11¹ × 43¹

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 1419

List of positive integer factors of 1419 that divides 1400 without a remainder.

1, 3, 11, 33, 43, 129, 473

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1400 and 1419. The biggest common factor number is the GCF number.
So the greatest common factor 1400 and 1419 is 1.

Also check out the Least Common Multiple of 1400 and 1419