What is the Greatest Common Factor of 1386 and 1400?

Greatest common factor (GCF) of 1386 and 1400 is 14.

GCF(1386,1400) = 14

We will now calculate the prime factors of 1386 and 1400, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1386 and 1400.

How to find the GCF of 1386 and 1400?

We will first find the prime factorization of 1386 and 1400. After we will calculate the factors of 1386 and 1400 and find the biggest common factor number .

Step-1: Prime Factorization of 1386

Prime factors of 1386 are 2, 3, 7, 11. Prime factorization of 1386 in exponential form is:

1386 = 2¹ × 3² × 7¹ × 11¹

Step-2: 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-3: Factors of 1386

List of positive integer factors of 1386 that divides 1386 without a remainder.

1, 2, 3, 6, 7, 9, 11, 14, 18, 21, 22, 33, 42, 63, 66, 77, 99, 126, 154, 198, 231, 462, 693

Step-4: Factors of 1400

List of positive integer factors of 1400 that divides 1386 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1386 and 1400. The biggest common factor number is the GCF number.
So the greatest common factor 1386 and 1400 is 14.

Also check out the Least Common Multiple of 1386 and 1400