What is the Greatest Common Factor of 7725 and 7731?

Greatest common factor (GCF) of 7725 and 7731 is 3.

GCF(7725,7731) = 3

We will now calculate the prime factors of 7725 and 7731, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7725 and 7731.

How to find the GCF of 7725 and 7731?

We will first find the prime factorization of 7725 and 7731. After we will calculate the factors of 7725 and 7731 and find the biggest common factor number .

Step-1: Prime Factorization of 7725

Prime factors of 7725 are 3, 5, 103. Prime factorization of 7725 in exponential form is:

7725 = 3¹ × 5² × 103¹

Step-2: Prime Factorization of 7731

Prime factors of 7731 are 3, 859. Prime factorization of 7731 in exponential form is:

7731 = 3² × 859¹

Step-3: Factors of 7725

List of positive integer factors of 7725 that divides 7725 without a remainder.

1, 3, 5, 15, 25, 75, 103, 309, 515, 1545, 2575

Step-4: Factors of 7731

List of positive integer factors of 7731 that divides 7725 without a remainder.

1, 3, 9, 859, 2577

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7725 and 7731. The biggest common factor number is the GCF number.
So the greatest common factor 7725 and 7731 is 3.

Also check out the Least Common Multiple of 7725 and 7731