What is the Greatest Common Factor of 7546 and 7564?

Greatest common factor (GCF) of 7546 and 7564 is 2.

GCF(7546,7564) = 2

We will now calculate the prime factors of 7546 and 7564, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 7546 and 7564.

How to find the GCF of 7546 and 7564?

We will first find the prime factorization of 7546 and 7564. After we will calculate the factors of 7546 and 7564 and find the biggest common factor number .

Step-1: Prime Factorization of 7546

Prime factors of 7546 are 2, 7, 11. Prime factorization of 7546 in exponential form is:

7546 = 2¹ × 7³ × 11¹

Step-2: Prime Factorization of 7564

Prime factors of 7564 are 2, 31, 61. Prime factorization of 7564 in exponential form is:

7564 = 2² × 31¹ × 61¹

Step-3: Factors of 7546

List of positive integer factors of 7546 that divides 7546 without a remainder.

1, 2, 7, 11, 14, 22, 49, 77, 98, 154, 343, 539, 686, 1078, 3773

Step-4: Factors of 7564

List of positive integer factors of 7564 that divides 7546 without a remainder.

1, 2, 4, 31, 61, 62, 122, 124, 244, 1891, 3782

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 7546 and 7564. The biggest common factor number is the GCF number.
So the greatest common factor 7546 and 7564 is 2.

Also check out the Least Common Multiple of 7546 and 7564