What is the Greatest Common Factor of 34140 and 34144?

Greatest common factor (GCF) of 34140 and 34144 is 4.

GCF(34140,34144) = 4

We will now calculate the prime factors of 34140 and 34144, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34140 and 34144.

How to find the GCF of 34140 and 34144?

We will first find the prime factorization of 34140 and 34144. After we will calculate the factors of 34140 and 34144 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 34144

Prime factors of 34144 are 2, 11, 97. Prime factorization of 34144 in exponential form is:

34144 = 2⁵ × 11¹ × 97¹

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 34144

List of positive integer factors of 34144 that divides 34140 without a remainder.

1, 2, 4, 8, 11, 16, 22, 32, 44, 88, 97, 176, 194, 352, 388, 776, 1067, 1552, 2134, 3104, 4268, 8536, 17072

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34140 and 34144. The biggest common factor number is the GCF number.
So the greatest common factor 34140 and 34144 is 4.

Also check out the Least Common Multiple of 34140 and 34144