What is the Greatest Common Factor of 5625 and 5643?

Greatest common factor (GCF) of 5625 and 5643 is 9.

GCF(5625,5643) = 9

We will now calculate the prime factors of 5625 and 5643, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5625 and 5643.

How to find the GCF of 5625 and 5643?

We will first find the prime factorization of 5625 and 5643. After we will calculate the factors of 5625 and 5643 and find the biggest common factor number .

Step-1: Prime Factorization of 5625

Prime factors of 5625 are 3, 5. Prime factorization of 5625 in exponential form is:

5625 = 3² × 5⁴

Step-2: Prime Factorization of 5643

Prime factors of 5643 are 3, 11, 19. Prime factorization of 5643 in exponential form is:

5643 = 3³ × 11¹ × 19¹

Step-3: Factors of 5625

List of positive integer factors of 5625 that divides 5625 without a remainder.

1, 3, 5, 9, 15, 25, 45, 75, 125, 225, 375, 625, 1125, 1875

Step-4: Factors of 5643

List of positive integer factors of 5643 that divides 5625 without a remainder.

1, 3, 9, 11, 19, 27, 33, 57, 99, 171, 209, 297, 513, 627, 1881

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5625 and 5643. The biggest common factor number is the GCF number.
So the greatest common factor 5625 and 5643 is 9.

Also check out the Least Common Multiple of 5625 and 5643