What is the Greatest Common Factor of 17574 and 17582?

Greatest common factor (GCF) of 17574 and 17582 is 2.

GCF(17574,17582) = 2

We will now calculate the prime factors of 17574 and 17582, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17574 and 17582.

How to find the GCF of 17574 and 17582?

We will first find the prime factorization of 17574 and 17582. After we will calculate the factors of 17574 and 17582 and find the biggest common factor number .

Step-1: Prime Factorization of 17574

Prime factors of 17574 are 2, 3, 29, 101. Prime factorization of 17574 in exponential form is:

17574 = 2¹ × 3¹ × 29¹ × 101¹

Step-2: Prime Factorization of 17582

Prime factors of 17582 are 2, 59, 149. Prime factorization of 17582 in exponential form is:

17582 = 2¹ × 59¹ × 149¹

Step-3: Factors of 17574

List of positive integer factors of 17574 that divides 17574 without a remainder.

1, 2, 3, 6, 29, 58, 87, 101, 174, 202, 303, 606, 2929, 5858, 8787

Step-4: Factors of 17582

List of positive integer factors of 17582 that divides 17574 without a remainder.

1, 2, 59, 118, 149, 298, 8791

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17574 and 17582. The biggest common factor number is the GCF number.
So the greatest common factor 17574 and 17582 is 2.

Also check out the Least Common Multiple of 17574 and 17582