What is the Greatest Common Factor of 34140 and 34146?

Greatest common factor (GCF) of 34140 and 34146 is 6.

GCF(34140,34146) = 6

We will now calculate the prime factors of 34140 and 34146, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34140 and 34146.

How to find the GCF of 34140 and 34146?

We will first find the prime factorization of 34140 and 34146. After we will calculate the factors of 34140 and 34146 and find the biggest common factor number .

Step-1: Prime Factorization of 34140

Prime factors of 34140 are 2, 3, 5, 569. Prime factorization of 34140 in exponential form is:

34140 = 2² × 3¹ × 5¹ × 569¹

Step-2: Prime Factorization of 34146

Prime factors of 34146 are 2, 3, 7, 271. Prime factorization of 34146 in exponential form is:

34146 = 2¹ × 3² × 7¹ × 271¹

Step-3: Factors of 34140

List of positive integer factors of 34140 that divides 34140 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 569, 1138, 1707, 2276, 2845, 3414, 5690, 6828, 8535, 11380, 17070

Step-4: Factors of 34146

List of positive integer factors of 34146 that divides 34140 without a remainder.

1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126, 271, 542, 813, 1626, 1897, 2439, 3794, 4878, 5691, 11382, 17073

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34140 and 34146. The biggest common factor number is the GCF number.
So the greatest common factor 34140 and 34146 is 6.

Also check out the Least Common Multiple of 34140 and 34146