What is the Greatest Common Factor of 16100 and 16114?

Greatest common factor (GCF) of 16100 and 16114 is 14.

GCF(16100,16114) = 14

We will now calculate the prime factors of 16100 and 16114, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 16100 and 16114.

How to find the GCF of 16100 and 16114?

We will first find the prime factorization of 16100 and 16114. After we will calculate the factors of 16100 and 16114 and find the biggest common factor number .

Step-1: Prime Factorization of 16100

Prime factors of 16100 are 2, 5, 7, 23. Prime factorization of 16100 in exponential form is:

16100 = 2² × 5² × 7¹ × 23¹

Step-2: 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-3: Factors of 16100

List of positive integer factors of 16100 that divides 16100 without a remainder.

1, 2, 4, 5, 7, 10, 14, 20, 23, 25, 28, 35, 46, 50, 70, 92, 100, 115, 140, 161, 175, 230, 322, 350, 460, 575, 644, 700, 805, 1150, 1610, 2300, 3220, 4025, 8050

Step-4: Factors of 16114

List of positive integer factors of 16114 that divides 16100 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 16100 and 16114. The biggest common factor number is the GCF number.
So the greatest common factor 16100 and 16114 is 14.

Also check out the Least Common Multiple of 16100 and 16114