What is the Greatest Common Factor of 1725 and 1731?

Greatest common factor (GCF) of 1725 and 1731 is 3.

GCF(1725,1731) = 3

We will now calculate the prime factors of 1725 and 1731, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1725 and 1731.

How to find the GCF of 1725 and 1731?

We will first find the prime factorization of 1725 and 1731. After we will calculate the factors of 1725 and 1731 and find the biggest common factor number .

Step-1: Prime Factorization of 1725

Prime factors of 1725 are 3, 5, 23. Prime factorization of 1725 in exponential form is:

1725 = 3¹ × 5² × 23¹

Step-2: Prime Factorization of 1731

Prime factors of 1731 are 3, 577. Prime factorization of 1731 in exponential form is:

1731 = 3¹ × 577¹

Step-3: Factors of 1725

List of positive integer factors of 1725 that divides 1725 without a remainder.

1, 3, 5, 15, 23, 25, 69, 75, 115, 345, 575

Step-4: Factors of 1731

List of positive integer factors of 1731 that divides 1725 without a remainder.

1, 3, 577

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1725 and 1731. The biggest common factor number is the GCF number.
So the greatest common factor 1725 and 1731 is 3.

Also check out the Least Common Multiple of 1725 and 1731