What is the Greatest Common Factor of 34130 and 34140?

Greatest common factor (GCF) of 34130 and 34140 is 10.

GCF(34130,34140) = 10

We will now calculate the prime factors of 34130 and 34140, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34130 and 34140.

How to find the GCF of 34130 and 34140?

We will first find the prime factorization of 34130 and 34140. After we will calculate the factors of 34130 and 34140 and find the biggest common factor number .

Step-1: Prime Factorization of 34130

Prime factors of 34130 are 2, 5, 3413. Prime factorization of 34130 in exponential form is:

34130 = 2¹ × 5¹ × 3413¹

Step-2: 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-3: Factors of 34130

List of positive integer factors of 34130 that divides 34130 without a remainder.

1, 2, 5, 10, 3413, 6826, 17065

Step-4: Factors of 34140

List of positive integer factors of 34140 that divides 34130 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34130 and 34140. The biggest common factor number is the GCF number.
So the greatest common factor 34130 and 34140 is 10.

Also check out the Least Common Multiple of 34130 and 34140