What is the Greatest Common Factor of 17374 and 17388?

Greatest common factor (GCF) of 17374 and 17388 is 14.

GCF(17374,17388) = 14

We will now calculate the prime factors of 17374 and 17388, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17374 and 17388.

How to find the GCF of 17374 and 17388?

We will first find the prime factorization of 17374 and 17388. After we will calculate the factors of 17374 and 17388 and find the biggest common factor number .

Step-1: Prime Factorization of 17374

Prime factors of 17374 are 2, 7, 17, 73. Prime factorization of 17374 in exponential form is:

17374 = 2¹ × 7¹ × 17¹ × 73¹

Step-2: Prime Factorization of 17388

Prime factors of 17388 are 2, 3, 7, 23. Prime factorization of 17388 in exponential form is:

17388 = 2² × 3³ × 7¹ × 23¹

Step-3: Factors of 17374

List of positive integer factors of 17374 that divides 17374 without a remainder.

1, 2, 7, 14, 17, 34, 73, 119, 146, 238, 511, 1022, 1241, 2482, 8687

Step-4: Factors of 17388

List of positive integer factors of 17388 that divides 17374 without a remainder.

1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 23, 27, 28, 36, 42, 46, 54, 63, 69, 84, 92, 108, 126, 138, 161, 189, 207, 252, 276, 322, 378, 414, 483, 621, 644, 756, 828, 966, 1242, 1449, 1932, 2484, 2898, 4347, 5796, 8694

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17374 and 17388. The biggest common factor number is the GCF number.
So the greatest common factor 17374 and 17388 is 14.

Also check out the Least Common Multiple of 17374 and 17388