What is the Greatest Common Factor of 17834 and 17850?

Greatest common factor (GCF) of 17834 and 17850 is 2.

GCF(17834,17850) = 2

We will now calculate the prime factors of 17834 and 17850, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17834 and 17850.

How to find the GCF of 17834 and 17850?

We will first find the prime factorization of 17834 and 17850. After we will calculate the factors of 17834 and 17850 and find the biggest common factor number .

Step-1: Prime Factorization of 17834

Prime factors of 17834 are 2, 37, 241. Prime factorization of 17834 in exponential form is:

17834 = 2¹ × 37¹ × 241¹

Step-2: Prime Factorization of 17850

Prime factors of 17850 are 2, 3, 5, 7, 17. Prime factorization of 17850 in exponential form is:

17850 = 2¹ × 3¹ × 5² × 7¹ × 17¹

Step-3: Factors of 17834

List of positive integer factors of 17834 that divides 17834 without a remainder.

1, 2, 37, 74, 241, 482, 8917

Step-4: Factors of 17850

List of positive integer factors of 17850 that divides 17834 without a remainder.

1, 2, 3, 5, 6, 7, 10, 14, 15, 17, 21, 25, 30, 34, 35, 42, 50, 51, 70, 75, 85, 102, 105, 119, 150, 170, 175, 210, 238, 255, 350, 357, 425, 510, 525, 595, 714, 850, 1050, 1190, 1275, 1785, 2550, 2975, 3570, 5950, 8925

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17834 and 17850. The biggest common factor number is the GCF number.
So the greatest common factor 17834 and 17850 is 2.

Also check out the Least Common Multiple of 17834 and 17850