What is the Greatest Common Factor of 1563 and 1575?

Greatest common factor (GCF) of 1563 and 1575 is 3.

GCF(1563,1575) = 3

We will now calculate the prime factors of 1563 and 1575, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 1563 and 1575.

How to find the GCF of 1563 and 1575?

We will first find the prime factorization of 1563 and 1575. After we will calculate the factors of 1563 and 1575 and find the biggest common factor number .

Step-1: Prime Factorization of 1563

Prime factors of 1563 are 3, 521. Prime factorization of 1563 in exponential form is:

1563 = 3¹ × 521¹

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 1563

List of positive integer factors of 1563 that divides 1563 without a remainder.

1, 3, 521

Step-4: Factors of 1575

List of positive integer factors of 1575 that divides 1563 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 1563 and 1575. The biggest common factor number is the GCF number.
So the greatest common factor 1563 and 1575 is 3.

Also check out the Least Common Multiple of 1563 and 1575