What is the Greatest Common Factor of 1688 and 1700?

Greatest common factor (GCF) of 1688 and 1700 is 4.

GCF(1688,1700) = 4

We will now calculate the prime factors of 1688 and 1700, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1688 and 1700.

How to find the GCF of 1688 and 1700?

We will first find the prime factorization of 1688 and 1700. After we will calculate the factors of 1688 and 1700 and find the biggest common factor number .

Step-1: Prime Factorization of 1688

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

1688 = 2³ × 211¹

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 1688

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

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

Step-4: Factors of 1700

List of positive integer factors of 1700 that divides 1688 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 1688 and 1700. The biggest common factor number is the GCF number.
So the greatest common factor 1688 and 1700 is 4.

Also check out the Least Common Multiple of 1688 and 1700