What is the Greatest Common Factor of 5643 and 5654?

Greatest common factor (GCF) of 5643 and 5654 is 11.

GCF(5643,5654) = 11

We will now calculate the prime factors of 5643 and 5654, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5643 and 5654.

How to find the GCF of 5643 and 5654?

We will first find the prime factorization of 5643 and 5654. After we will calculate the factors of 5643 and 5654 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 5654

Prime factors of 5654 are 2, 11, 257. Prime factorization of 5654 in exponential form is:

5654 = 2¹ × 11¹ × 257¹

Step-3: Factors of 5643

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

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

Step-4: Factors of 5654

List of positive integer factors of 5654 that divides 5643 without a remainder.

1, 2, 11, 22, 257, 514, 2827

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5643 and 5654. The biggest common factor number is the GCF number.
So the greatest common factor 5643 and 5654 is 11.

Also check out the Least Common Multiple of 5643 and 5654