What is the Greatest Common Factor of 1664 and 1677?

Greatest common factor (GCF) of 1664 and 1677 is 13.

GCF(1664,1677) = 13

We will now calculate the prime factors of 1664 and 1677, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1664 and 1677.

How to find the GCF of 1664 and 1677?

We will first find the prime factorization of 1664 and 1677. After we will calculate the factors of 1664 and 1677 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 1677

Prime factors of 1677 are 3, 13, 43. Prime factorization of 1677 in exponential form is:

1677 = 3¹ × 13¹ × 43¹

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 1677

List of positive integer factors of 1677 that divides 1664 without a remainder.

1, 3, 13, 39, 43, 129, 559

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1664 and 1677. The biggest common factor number is the GCF number.
So the greatest common factor 1664 and 1677 is 13.

Also check out the Least Common Multiple of 1664 and 1677