What is the Greatest Common Factor of 699 and 705?

Greatest common factor (GCF) of 699 and 705 is 3.

GCF(699,705) = 3

We will now calculate the prime factors of 699 and 705, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 699 and 705.

How to find the GCF of 699 and 705?

We will first find the prime factorization of 699 and 705. After we will calculate the factors of 699 and 705 and find the biggest common factor number .

Step-1: Prime Factorization of 699

Prime factors of 699 are 3, 233. Prime factorization of 699 in exponential form is:

699 = 3¹ × 233¹

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 699

List of positive integer factors of 699 that divides 699 without a remainder.

1, 3, 233

Step-4: Factors of 705

List of positive integer factors of 705 that divides 699 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 699 and 705. The biggest common factor number is the GCF number.
So the greatest common factor 699 and 705 is 3.

Also check out the Least Common Multiple of 699 and 705