What is the Greatest Common Factor of 1664 and 1678?

Greatest common factor (GCF) of 1664 and 1678 is 2.

GCF(1664,1678) = 2

We will now calculate the prime factors of 1664 and 1678, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1664 and 1678.

How to find the GCF of 1664 and 1678?

We will first find the prime factorization of 1664 and 1678. After we will calculate the factors of 1664 and 1678 and find the biggest common factor number .

Step-1: Prime Factorization of 1664

Prime factors of 1664 are 2, 13. Prime factorization of 1664 in exponential form is:

1664 = 2⁷ × 13¹

Step-2: Prime Factorization of 1678

Prime factors of 1678 are 2, 839. Prime factorization of 1678 in exponential form is:

1678 = 2¹ × 839¹

Step-3: Factors of 1664

List of positive integer factors of 1664 that divides 1664 without a remainder.

1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 128, 208, 416, 832

Step-4: Factors of 1678

List of positive integer factors of 1678 that divides 1664 without a remainder.

1, 2, 839

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1664 and 1678. The biggest common factor number is the GCF number.
So the greatest common factor 1664 and 1678 is 2.

Also check out the Least Common Multiple of 1664 and 1678