What is the Greatest Common Factor of 1564 and 1575?

Greatest common factor (GCF) of 1564 and 1575 is 1.

GCF(1564,1575) = 1

We will now calculate the prime factors of 1564 and 1575, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1564 and 1575.

How to find the GCF of 1564 and 1575?

We will first find the prime factorization of 1564 and 1575. After we will calculate the factors of 1564 and 1575 and find the biggest common factor number .

Step-1: Prime Factorization of 1564

Prime factors of 1564 are 2, 17, 23. Prime factorization of 1564 in exponential form is:

1564 = 2² × 17¹ × 23¹

Step-2: Prime Factorization of 1575

Prime factors of 1575 are 3, 5, 7. Prime factorization of 1575 in exponential form is:

1575 = 3² × 5² × 7¹

Step-3: Factors of 1564

List of positive integer factors of 1564 that divides 1564 without a remainder.

1, 2, 4, 17, 23, 34, 46, 68, 92, 391, 782

Step-4: Factors of 1575

List of positive integer factors of 1575 that divides 1564 without a remainder.

1, 3, 5, 7, 9, 15, 21, 25, 35, 45, 63, 75, 105, 175, 225, 315, 525

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 1564 and 1575. The biggest common factor number is the GCF number.
So the greatest common factor 1564 and 1575 is 1.

Also check out the Least Common Multiple of 1564 and 1575