What is the Greatest Common Factor of 17878 and 17892?

Greatest common factor (GCF) of 17878 and 17892 is 14.

GCF(17878,17892) = 14

We will now calculate the prime factors of 17878 and 17892, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17878 and 17892.

How to find the GCF of 17878 and 17892?

We will first find the prime factorization of 17878 and 17892. After we will calculate the factors of 17878 and 17892 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 17892

Prime factors of 17892 are 2, 3, 7, 71. Prime factorization of 17892 in exponential form is:

17892 = 2² × 3² × 7¹ × 71¹

Step-3: Factors of 17878

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

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

Step-4: Factors of 17892

List of positive integer factors of 17892 that divides 17878 without a remainder.

1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 71, 84, 126, 142, 213, 252, 284, 426, 497, 639, 852, 994, 1278, 1491, 1988, 2556, 2982, 4473, 5964, 8946

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17878 and 17892. The biggest common factor number is the GCF number.
So the greatest common factor 17878 and 17892 is 14.

Also check out the Least Common Multiple of 17878 and 17892