What is the Greatest Common Factor of 7565 and 7582?

Greatest common factor (GCF) of 7565 and 7582 is 17.

GCF(7565,7582) = 17

We will now calculate the prime factors of 7565 and 7582, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7565 and 7582.

How to find the GCF of 7565 and 7582?

We will first find the prime factorization of 7565 and 7582. After we will calculate the factors of 7565 and 7582 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 7582

Prime factors of 7582 are 2, 17, 223. Prime factorization of 7582 in exponential form is:

7582 = 2¹ × 17¹ × 223¹

Step-3: Factors of 7565

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

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

Step-4: Factors of 7582

List of positive integer factors of 7582 that divides 7565 without a remainder.

1, 2, 17, 34, 223, 446, 3791

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7565 and 7582. The biggest common factor number is the GCF number.
So the greatest common factor 7565 and 7582 is 17.

Also check out the Least Common Multiple of 7565 and 7582