What is the Greatest Common Factor of 1705 and 1714?

Greatest common factor (GCF) of 1705 and 1714 is 1.

GCF(1705,1714) = 1

We will now calculate the prime factors of 1705 and 1714, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1705 and 1714.

How to find the GCF of 1705 and 1714?

We will first find the prime factorization of 1705 and 1714. After we will calculate the factors of 1705 and 1714 and find the biggest common factor number .

Step-1: Prime Factorization of 1705

Prime factors of 1705 are 5, 11, 31. Prime factorization of 1705 in exponential form is:

1705 = 5¹ × 11¹ × 31¹

Step-2: Prime Factorization of 1714

Prime factors of 1714 are 2, 857. Prime factorization of 1714 in exponential form is:

1714 = 2¹ × 857¹

Step-3: Factors of 1705

List of positive integer factors of 1705 that divides 1705 without a remainder.

1, 5, 11, 31, 55, 155, 341

Step-4: Factors of 1714

List of positive integer factors of 1714 that divides 1705 without a remainder.

1, 2, 857

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1705 and 1714. The biggest common factor number is the GCF number.
So the greatest common factor 1705 and 1714 is 1.

Also check out the Least Common Multiple of 1705 and 1714