What is the Greatest Common Factor of 34160 and 34174?

Greatest common factor (GCF) of 34160 and 34174 is 14.

GCF(34160,34174) = 14

We will now calculate the prime factors of 34160 and 34174, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34160 and 34174.

How to find the GCF of 34160 and 34174?

We will first find the prime factorization of 34160 and 34174. After we will calculate the factors of 34160 and 34174 and find the biggest common factor number .

Step-1: Prime Factorization of 34160

Prime factors of 34160 are 2, 5, 7, 61. Prime factorization of 34160 in exponential form is:

34160 = 2⁴ × 5¹ × 7¹ × 61¹

Step-2: Prime Factorization of 34174

Prime factors of 34174 are 2, 7, 2441. Prime factorization of 34174 in exponential form is:

34174 = 2¹ × 7¹ × 2441¹

Step-3: Factors of 34160

List of positive integer factors of 34160 that divides 34160 without a remainder.

1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 56, 61, 70, 80, 112, 122, 140, 244, 280, 305, 427, 488, 560, 610, 854, 976, 1220, 1708, 2135, 2440, 3416, 4270, 4880, 6832, 8540, 17080

Step-4: Factors of 34174

List of positive integer factors of 34174 that divides 34160 without a remainder.

1, 2, 7, 14, 2441, 4882, 17087

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34160 and 34174. The biggest common factor number is the GCF number.
So the greatest common factor 34160 and 34174 is 14.

Also check out the Least Common Multiple of 34160 and 34174