What is the Greatest Common Factor of 688 and 705?

Greatest common factor (GCF) of 688 and 705 is 1.

GCF(688,705) = 1

We will now calculate the prime factors of 688 and 705, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 688 and 705.

How to find the GCF of 688 and 705?

We will first find the prime factorization of 688 and 705. After we will calculate the factors of 688 and 705 and find the biggest common factor number .

Step-1: Prime Factorization of 688

Prime factors of 688 are 2, 43. Prime factorization of 688 in exponential form is:

688 = 2⁴ × 43¹

Step-2: Prime Factorization of 705

Prime factors of 705 are 3, 5, 47. Prime factorization of 705 in exponential form is:

705 = 3¹ × 5¹ × 47¹

Step-3: Factors of 688

List of positive integer factors of 688 that divides 688 without a remainder.

1, 2, 4, 8, 16, 43, 86, 172, 344

Step-4: Factors of 705

List of positive integer factors of 705 that divides 688 without a remainder.

1, 3, 5, 15, 47, 141, 235

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 688 and 705. The biggest common factor number is the GCF number.
So the greatest common factor 688 and 705 is 1.

Also check out the Least Common Multiple of 688 and 705