What is the Greatest Common Factor of 17673 and 17688?

Greatest common factor (GCF) of 17673 and 17688 is 3.

GCF(17673,17688) = 3

We will now calculate the prime factors of 17673 and 17688, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17673 and 17688.

How to find the GCF of 17673 and 17688?

We will first find the prime factorization of 17673 and 17688. After we will calculate the factors of 17673 and 17688 and find the biggest common factor number .

Step-1: Prime Factorization of 17673

Prime factors of 17673 are 3, 43, 137. Prime factorization of 17673 in exponential form is:

17673 = 3¹ × 43¹ × 137¹

Step-2: Prime Factorization of 17688

Prime factors of 17688 are 2, 3, 11, 67. Prime factorization of 17688 in exponential form is:

17688 = 2³ × 3¹ × 11¹ × 67¹

Step-3: Factors of 17673

List of positive integer factors of 17673 that divides 17673 without a remainder.

1, 3, 43, 129, 137, 411, 5891

Step-4: Factors of 17688

List of positive integer factors of 17688 that divides 17673 without a remainder.

1, 2, 3, 4, 6, 8, 11, 12, 22, 24, 33, 44, 66, 67, 88, 132, 134, 201, 264, 268, 402, 536, 737, 804, 1474, 1608, 2211, 2948, 4422, 5896, 8844

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17673 and 17688. The biggest common factor number is the GCF number.
So the greatest common factor 17673 and 17688 is 3.

Also check out the Least Common Multiple of 17673 and 17688