What is the Greatest Common Factor of 1664 and 1682?

Greatest common factor (GCF) of 1664 and 1682 is 2.

GCF(1664,1682) = 2

We will now calculate the prime factors of 1664 and 1682, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1664 and 1682.

How to find the GCF of 1664 and 1682?

We will first find the prime factorization of 1664 and 1682. After we will calculate the factors of 1664 and 1682 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 1682

Prime factors of 1682 are 2, 29. Prime factorization of 1682 in exponential form is:

1682 = 2¹ × 29²

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 1682

List of positive integer factors of 1682 that divides 1664 without a remainder.

1, 2, 29, 58, 841

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1664 and 1682. The biggest common factor number is the GCF number.
So the greatest common factor 1664 and 1682 is 2.

Also check out the Least Common Multiple of 1664 and 1682