What is the Greatest Common Factor of 17619 and 17633?

Greatest common factor (GCF) of 17619 and 17633 is 7.

GCF(17619,17633) = 7

We will now calculate the prime factors of 17619 and 17633, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17619 and 17633.

How to find the GCF of 17619 and 17633?

We will first find the prime factorization of 17619 and 17633. After we will calculate the factors of 17619 and 17633 and find the biggest common factor number .

Step-1: Prime Factorization of 17619

Prime factors of 17619 are 3, 7, 839. Prime factorization of 17619 in exponential form is:

17619 = 3¹ × 7¹ × 839¹

Step-2: Prime Factorization of 17633

Prime factors of 17633 are 7, 11, 229. Prime factorization of 17633 in exponential form is:

17633 = 7¹ × 11¹ × 229¹

Step-3: Factors of 17619

List of positive integer factors of 17619 that divides 17619 without a remainder.

1, 3, 7, 21, 839, 2517, 5873

Step-4: Factors of 17633

List of positive integer factors of 17633 that divides 17619 without a remainder.

1, 7, 11, 77, 229, 1603, 2519

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17619 and 17633. The biggest common factor number is the GCF number.
So the greatest common factor 17619 and 17633 is 7.

Also check out the Least Common Multiple of 17619 and 17633