What is the Greatest Common Factor of 1400 and 1408?

Greatest common factor (GCF) of 1400 and 1408 is 8.

GCF(1400,1408) = 8

We will now calculate the prime factors of 1400 and 1408, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1400 and 1408.

How to find the GCF of 1400 and 1408?

We will first find the prime factorization of 1400 and 1408. After we will calculate the factors of 1400 and 1408 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 1408

Prime factors of 1408 are 2, 11. Prime factorization of 1408 in exponential form is:

1408 = 2⁷ × 11¹

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 1408

List of positive integer factors of 1408 that divides 1400 without a remainder.

1, 2, 4, 8, 11, 16, 22, 32, 44, 64, 88, 128, 176, 352, 704

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1400 and 1408. The biggest common factor number is the GCF number.
So the greatest common factor 1400 and 1408 is 8.

Also check out the Least Common Multiple of 1400 and 1408