What is the Greatest Common Factor of 1705 and 1720?

Greatest common factor (GCF) of 1705 and 1720 is 5.

GCF(1705,1720) = 5

We will now calculate the prime factors of 1705 and 1720, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1705 and 1720.

How to find the GCF of 1705 and 1720?

We will first find the prime factorization of 1705 and 1720. After we will calculate the factors of 1705 and 1720 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 1720

Prime factors of 1720 are 2, 5, 43. Prime factorization of 1720 in exponential form is:

1720 = 2³ × 5¹ × 43¹

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 1720

List of positive integer factors of 1720 that divides 1705 without a remainder.

1, 2, 4, 5, 8, 10, 20, 40, 43, 86, 172, 215, 344, 430, 860

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1705 and 1720. The biggest common factor number is the GCF number.
So the greatest common factor 1705 and 1720 is 5.

Also check out the Least Common Multiple of 1705 and 1720