What is the Greatest Common Factor of 17914 and 17932?

Greatest common factor (GCF) of 17914 and 17932 is 2.

GCF(17914,17932) = 2

We will now calculate the prime factors of 17914 and 17932, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17914 and 17932.

How to find the GCF of 17914 and 17932?

We will first find the prime factorization of 17914 and 17932. After we will calculate the factors of 17914 and 17932 and find the biggest common factor number .

Step-1: Prime Factorization of 17914

Prime factors of 17914 are 2, 13, 53. Prime factorization of 17914 in exponential form is:

17914 = 2¹ × 13² × 53¹

Step-2: Prime Factorization of 17932

Prime factors of 17932 are 2, 4483. Prime factorization of 17932 in exponential form is:

17932 = 2² × 4483¹

Step-3: Factors of 17914

List of positive integer factors of 17914 that divides 17914 without a remainder.

1, 2, 13, 26, 53, 106, 169, 338, 689, 1378, 8957

Step-4: Factors of 17932

List of positive integer factors of 17932 that divides 17914 without a remainder.

1, 2, 4, 4483, 8966

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17914 and 17932. The biggest common factor number is the GCF number.
So the greatest common factor 17914 and 17932 is 2.

Also check out the Least Common Multiple of 17914 and 17932