What is the Greatest Common Factor of 7569 and 7575?

Greatest common factor (GCF) of 7569 and 7575 is 3.

GCF(7569,7575) = 3

We will now calculate the prime factors of 7569 and 7575, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7569 and 7575.

How to find the GCF of 7569 and 7575?

We will first find the prime factorization of 7569 and 7575. After we will calculate the factors of 7569 and 7575 and find the biggest common factor number .

Step-1: Prime Factorization of 7569

Prime factors of 7569 are 3, 29. Prime factorization of 7569 in exponential form is:

7569 = 3² × 29²

Step-2: Prime Factorization of 7575

Prime factors of 7575 are 3, 5, 101. Prime factorization of 7575 in exponential form is:

7575 = 3¹ × 5² × 101¹

Step-3: Factors of 7569

List of positive integer factors of 7569 that divides 7569 without a remainder.

1, 3, 9, 29, 87, 261, 841, 2523

Step-4: Factors of 7575

List of positive integer factors of 7575 that divides 7569 without a remainder.

1, 3, 5, 15, 25, 75, 101, 303, 505, 1515, 2525

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7569 and 7575. The biggest common factor number is the GCF number.
So the greatest common factor 7569 and 7575 is 3.

Also check out the Least Common Multiple of 7569 and 7575