What is the Greatest Common Factor of 34144 and 34160?

Greatest common factor (GCF) of 34144 and 34160 is 16.

GCF(34144,34160) = 16

We will now calculate the prime factors of 34144 and 34160, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 34144 and 34160.

How to find the GCF of 34144 and 34160?

We will first find the prime factorization of 34144 and 34160. After we will calculate the factors of 34144 and 34160 and find the biggest common factor number .

Step-1: 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-2: 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-3: Factors of 34144

List of positive integer factors of 34144 that divides 34144 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

Step-4: Factors of 34160

List of positive integer factors of 34160 that divides 34144 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 34144 and 34160. The biggest common factor number is the GCF number.
So the greatest common factor 34144 and 34160 is 16.

Also check out the Least Common Multiple of 34144 and 34160