What is the Greatest Common Factor of 1688 and 1704?

Greatest common factor (GCF) of 1688 and 1704 is 8.

GCF(1688,1704) = 8

We will now calculate the prime factors of 1688 and 1704, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1688 and 1704.

How to find the GCF of 1688 and 1704?

We will first find the prime factorization of 1688 and 1704. After we will calculate the factors of 1688 and 1704 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 1704

Prime factors of 1704 are 2, 3, 71. Prime factorization of 1704 in exponential form is:

1704 = 2³ × 3¹ × 71¹

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 1704

List of positive integer factors of 1704 that divides 1688 without a remainder.

1, 2, 3, 4, 6, 8, 12, 24, 71, 142, 213, 284, 426, 568, 852

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1688 and 1704. The biggest common factor number is the GCF number.
So the greatest common factor 1688 and 1704 is 8.

Also check out the Least Common Multiple of 1688 and 1704