What is the Greatest Common Factor of 1680 and 1700?

Greatest common factor (GCF) of 1680 and 1700 is 20.

GCF(1680,1700) = 20

We will now calculate the prime factors of 1680 and 1700, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1680 and 1700.

How to find the GCF of 1680 and 1700?

We will first find the prime factorization of 1680 and 1700. After we will calculate the factors of 1680 and 1700 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 1700

Prime factors of 1700 are 2, 5, 17. Prime factorization of 1700 in exponential form is:

1700 = 2² × 5² × 17¹

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 1700

List of positive integer factors of 1700 that divides 1680 without a remainder.

1, 2, 4, 5, 10, 17, 20, 25, 34, 50, 68, 85, 100, 170, 340, 425, 850

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1680 and 1700. The biggest common factor number is the GCF number.
So the greatest common factor 1680 and 1700 is 20.

Also check out the Least Common Multiple of 1680 and 1700