What is the Greatest Common Factor of 1380 and 1400?

Greatest common factor (GCF) of 1380 and 1400 is 20.

GCF(1380,1400) = 20

We will now calculate the prime factors of 1380 and 1400, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1380 and 1400.

How to find the GCF of 1380 and 1400?

We will first find the prime factorization of 1380 and 1400. After we will calculate the factors of 1380 and 1400 and find the biggest common factor number .

Step-1: Prime Factorization of 1380

Prime factors of 1380 are 2, 3, 5, 23. Prime factorization of 1380 in exponential form is:

1380 = 2² × 3¹ × 5¹ × 23¹

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 1380

List of positive integer factors of 1380 that divides 1380 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 23, 30, 46, 60, 69, 92, 115, 138, 230, 276, 345, 460, 690

Step-4: Factors of 1400

List of positive integer factors of 1400 that divides 1380 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 1380 and 1400. The biggest common factor number is the GCF number.
So the greatest common factor 1380 and 1400 is 20.

Also check out the Least Common Multiple of 1380 and 1400