What is the Greatest Common Factor of 1680 and 1688?

Greatest common factor (GCF) of 1680 and 1688 is 8.

GCF(1680,1688) = 8

We will now calculate the prime factors of 1680 and 1688, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1680 and 1688.

How to find the GCF of 1680 and 1688?

We will first find the prime factorization of 1680 and 1688. After we will calculate the factors of 1680 and 1688 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 1688

Prime factors of 1688 are 2, 211. Prime factorization of 1688 in exponential form is:

1688 = 2³ × 211¹

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 1688

List of positive integer factors of 1688 that divides 1680 without a remainder.

1, 2, 4, 8, 211, 422, 844

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1680 and 1688. The biggest common factor number is the GCF number.
So the greatest common factor 1680 and 1688 is 8.

Also check out the Least Common Multiple of 1680 and 1688