What is the Greatest Common Factor of 1664 and 1680?

Greatest common factor (GCF) of 1664 and 1680 is 16.

GCF(1664,1680) = 16

We will now calculate the prime factors of 1664 and 1680, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1664 and 1680.

How to find the GCF of 1664 and 1680?

We will first find the prime factorization of 1664 and 1680. After we will calculate the factors of 1664 and 1680 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 1680

Prime factors of 1680 are 2, 3, 5, 7. Prime factorization of 1680 in exponential form is:

1680 = 2⁴ × 3¹ × 5¹ × 7¹

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 1680

List of positive integer factors of 1680 that divides 1664 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 35, 40, 42, 48, 56, 60, 70, 80, 84, 105, 112, 120, 140, 168, 210, 240, 280, 336, 420, 560, 840

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1664 and 1680. The biggest common factor number is the GCF number.
So the greatest common factor 1664 and 1680 is 16.

Also check out the Least Common Multiple of 1664 and 1680