What is the Greatest Common Factor of 7548 and 7565?

Greatest common factor (GCF) of 7548 and 7565 is 17.

GCF(7548,7565) = 17

We will now calculate the prime factors of 7548 and 7565, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7548 and 7565.

How to find the GCF of 7548 and 7565?

We will first find the prime factorization of 7548 and 7565. After we will calculate the factors of 7548 and 7565 and find the biggest common factor number .

Step-1: Prime Factorization of 7548

Prime factors of 7548 are 2, 3, 17, 37. Prime factorization of 7548 in exponential form is:

7548 = 2² × 3¹ × 17¹ × 37¹

Step-2: Prime Factorization of 7565

Prime factors of 7565 are 5, 17, 89. Prime factorization of 7565 in exponential form is:

7565 = 5¹ × 17¹ × 89¹

Step-3: Factors of 7548

List of positive integer factors of 7548 that divides 7548 without a remainder.

1, 2, 3, 4, 6, 12, 17, 34, 37, 51, 68, 74, 102, 111, 148, 204, 222, 444, 629, 1258, 1887, 2516, 3774

Step-4: Factors of 7565

List of positive integer factors of 7565 that divides 7548 without a remainder.

1, 5, 17, 85, 89, 445, 1513

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7548 and 7565. The biggest common factor number is the GCF number.
So the greatest common factor 7548 and 7565 is 17.

Also check out the Least Common Multiple of 7548 and 7565