What is the Greatest Common Factor of 3564 and 3575?

Greatest common factor (GCF) of 3564 and 3575 is 11.

GCF(3564,3575) = 11

We will now calculate the prime factors of 3564 and 3575, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 3564 and 3575.

How to find the GCF of 3564 and 3575?

We will first find the prime factorization of 3564 and 3575. After we will calculate the factors of 3564 and 3575 and find the biggest common factor number .

Step-1: Prime Factorization of 3564

Prime factors of 3564 are 2, 3, 11. Prime factorization of 3564 in exponential form is:

3564 = 2² × 3⁴ × 11¹

Step-2: Prime Factorization of 3575

Prime factors of 3575 are 5, 11, 13. Prime factorization of 3575 in exponential form is:

3575 = 5² × 11¹ × 13¹

Step-3: Factors of 3564

List of positive integer factors of 3564 that divides 3564 without a remainder.

1, 2, 3, 4, 6, 9, 11, 12, 18, 22, 27, 33, 36, 44, 54, 66, 81, 99, 108, 132, 162, 198, 297, 324, 396, 594, 891, 1188, 1782

Step-4: Factors of 3575

List of positive integer factors of 3575 that divides 3564 without a remainder.

1, 5, 11, 13, 25, 55, 65, 143, 275, 325, 715

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 3564 and 3575. The biggest common factor number is the GCF number.
So the greatest common factor 3564 and 3575 is 11.

Also check out the Least Common Multiple of 3564 and 3575