What is the Greatest Common Factor of 1408 and 1422?

Greatest common factor (GCF) of 1408 and 1422 is 2.

GCF(1408,1422) = 2

We will now calculate the prime factors of 1408 and 1422, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1408 and 1422.

How to find the GCF of 1408 and 1422?

We will first find the prime factorization of 1408 and 1422. After we will calculate the factors of 1408 and 1422 and find the biggest common factor number .

Step-1: Prime Factorization of 1408

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

1408 = 2⁷ × 11¹

Step-2: Prime Factorization of 1422

Prime factors of 1422 are 2, 3, 79. Prime factorization of 1422 in exponential form is:

1422 = 2¹ × 3² × 79¹

Step-3: Factors of 1408

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

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

Step-4: Factors of 1422

List of positive integer factors of 1422 that divides 1408 without a remainder.

1, 2, 3, 6, 9, 18, 79, 158, 237, 474, 711

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1408 and 1422. The biggest common factor number is the GCF number.
So the greatest common factor 1408 and 1422 is 2.

Also check out the Least Common Multiple of 1408 and 1422