What is the Greatest Common Factor of 1680 and 1684?

Greatest common factor (GCF) of 1680 and 1684 is 4.

GCF(1680,1684) = 4

We will now calculate the prime factors of 1680 and 1684, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1680 and 1684.

How to find the GCF of 1680 and 1684?

We will first find the prime factorization of 1680 and 1684. After we will calculate the factors of 1680 and 1684 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 1684

Prime factors of 1684 are 2, 421. Prime factorization of 1684 in exponential form is:

1684 = 2² × 421¹

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 1684

List of positive integer factors of 1684 that divides 1680 without a remainder.

1, 2, 4, 421, 842

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1680 and 1684. The biggest common factor number is the GCF number.
So the greatest common factor 1680 and 1684 is 4.

Also check out the Least Common Multiple of 1680 and 1684