What is the Greatest Common Factor of 17536 and 17549?

Greatest common factor (GCF) of 17536 and 17549 is 1.

GCF(17536,17549) = 1

We will now calculate the prime factors of 17536 and 17549, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17536 and 17549.

How to find the GCF of 17536 and 17549?

We will first find the prime factorization of 17536 and 17549. After we will calculate the factors of 17536 and 17549 and find the biggest common factor number .

Step-1: Prime Factorization of 17536

Prime factors of 17536 are 2, 137. Prime factorization of 17536 in exponential form is:

17536 = 2⁷ × 137¹

Step-2: Prime Factorization of 17549

Prime factors of 17549 are 7, 23, 109. Prime factorization of 17549 in exponential form is:

17549 = 7¹ × 23¹ × 109¹

Step-3: Factors of 17536

List of positive integer factors of 17536 that divides 17536 without a remainder.

1, 2, 4, 8, 16, 32, 64, 128, 137, 274, 548, 1096, 2192, 4384, 8768

Step-4: Factors of 17549

List of positive integer factors of 17549 that divides 17536 without a remainder.

1, 7, 23, 109, 161, 763, 2507

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17536 and 17549. The biggest common factor number is the GCF number.
So the greatest common factor 17536 and 17549 is 1.

Also check out the Least Common Multiple of 17536 and 17549