What is the Greatest Common Factor of 17854 and 17864?

Greatest common factor (GCF) of 17854 and 17864 is 2.

GCF(17854,17864) = 2

We will now calculate the prime factors of 17854 and 17864, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17854 and 17864.

How to find the GCF of 17854 and 17864?

We will first find the prime factorization of 17854 and 17864. After we will calculate the factors of 17854 and 17864 and find the biggest common factor number .

Step-1: Prime Factorization of 17854

Prime factors of 17854 are 2, 79, 113. Prime factorization of 17854 in exponential form is:

17854 = 2¹ × 79¹ × 113¹

Step-2: Prime Factorization of 17864

Prime factors of 17864 are 2, 7, 11, 29. Prime factorization of 17864 in exponential form is:

17864 = 2³ × 7¹ × 11¹ × 29¹

Step-3: Factors of 17854

List of positive integer factors of 17854 that divides 17854 without a remainder.

1, 2, 79, 113, 158, 226, 8927

Step-4: Factors of 17864

List of positive integer factors of 17864 that divides 17854 without a remainder.

1, 2, 4, 7, 8, 11, 14, 22, 28, 29, 44, 56, 58, 77, 88, 116, 154, 203, 232, 308, 319, 406, 616, 638, 812, 1276, 1624, 2233, 2552, 4466, 8932

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17854 and 17864. The biggest common factor number is the GCF number.
So the greatest common factor 17854 and 17864 is 2.

Also check out the Least Common Multiple of 17854 and 17864