What is the Greatest Common Factor of 16114 and 16128?

Greatest common factor (GCF) of 16114 and 16128 is 14.

GCF(16114,16128) = 14

We will now calculate the prime factors of 16114 and 16128, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 16114 and 16128.

How to find the GCF of 16114 and 16128?

We will first find the prime factorization of 16114 and 16128. After we will calculate the factors of 16114 and 16128 and find the biggest common factor number .

Step-1: Prime Factorization of 16114

Prime factors of 16114 are 2, 7, 1151. Prime factorization of 16114 in exponential form is:

16114 = 2¹ × 7¹ × 1151¹

Step-2: Prime Factorization of 16128

Prime factors of 16128 are 2, 3, 7. Prime factorization of 16128 in exponential form is:

16128 = 2⁸ × 3² × 7¹

Step-3: Factors of 16114

List of positive integer factors of 16114 that divides 16114 without a remainder.

1, 2, 7, 14, 1151, 2302, 8057

Step-4: Factors of 16128

List of positive integer factors of 16128 that divides 16114 without a remainder.

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 32, 36, 42, 48, 56, 63, 64, 72, 84, 96, 112, 126, 128, 144, 168, 192, 224, 252, 256, 288, 336, 384, 448, 504, 576, 672, 768, 896, 1008, 1152, 1344, 1792, 2016, 2304, 2688, 4032, 5376, 8064

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 16114 and 16128. The biggest common factor number is the GCF number.
So the greatest common factor 16114 and 16128 is 14.

Also check out the Least Common Multiple of 16114 and 16128