What is the Greatest Common Factor of 1680 and 1696?

Greatest common factor (GCF) of 1680 and 1696 is 16.

GCF(1680,1696) = 16

We will now calculate the prime factors of 1680 and 1696, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1680 and 1696.

How to find the GCF of 1680 and 1696?

We will first find the prime factorization of 1680 and 1696. After we will calculate the factors of 1680 and 1696 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 1696

Prime factors of 1696 are 2, 53. Prime factorization of 1696 in exponential form is:

1696 = 2⁵ × 53¹

Step-3: Factors of 1680

List of positive integer factors of 1680 that divides 1680 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

Step-4: Factors of 1696

List of positive integer factors of 1696 that divides 1680 without a remainder.

1, 2, 4, 8, 16, 32, 53, 106, 212, 424, 848

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1680 and 1696. The biggest common factor number is the GCF number.
So the greatest common factor 1680 and 1696 is 16.

Also check out the Least Common Multiple of 1680 and 1696