What is the Greatest Common Factor of 1680 and 1698?

Greatest common factor (GCF) of 1680 and 1698 is 6.

GCF(1680,1698) = 6

We will now calculate the prime factors of 1680 and 1698, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1680 and 1698.

How to find the GCF of 1680 and 1698?

We will first find the prime factorization of 1680 and 1698. After we will calculate the factors of 1680 and 1698 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 1698

Prime factors of 1698 are 2, 3, 283. Prime factorization of 1698 in exponential form is:

1698 = 2¹ × 3¹ × 283¹

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 1698

List of positive integer factors of 1698 that divides 1680 without a remainder.

1, 2, 3, 6, 283, 566, 849

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1680 and 1698. The biggest common factor number is the GCF number.
So the greatest common factor 1680 and 1698 is 6.

Also check out the Least Common Multiple of 1680 and 1698