What is the Greatest Common Factor of 17872 and 17878?

Greatest common factor (GCF) of 17872 and 17878 is 2.

GCF(17872,17878) = 2

We will now calculate the prime factors of 17872 and 17878, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17872 and 17878.

How to find the GCF of 17872 and 17878?

We will first find the prime factorization of 17872 and 17878. After we will calculate the factors of 17872 and 17878 and find the biggest common factor number .

Step-1: Prime Factorization of 17872

Prime factors of 17872 are 2, 1117. Prime factorization of 17872 in exponential form is:

17872 = 2⁴ × 1117¹

Step-2: Prime Factorization of 17878

Prime factors of 17878 are 2, 7, 1277. Prime factorization of 17878 in exponential form is:

17878 = 2¹ × 7¹ × 1277¹

Step-3: Factors of 17872

List of positive integer factors of 17872 that divides 17872 without a remainder.

1, 2, 4, 8, 16, 1117, 2234, 4468, 8936

Step-4: Factors of 17878

List of positive integer factors of 17878 that divides 17872 without a remainder.

1, 2, 7, 14, 1277, 2554, 8939

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17872 and 17878. The biggest common factor number is the GCF number.
So the greatest common factor 17872 and 17878 is 2.

Also check out the Least Common Multiple of 17872 and 17878