What is the Greatest Common Factor of 76100 and 76114?

Greatest common factor (GCF) of 76100 and 76114 is 2.

GCF(76100,76114) = 2

We will now calculate the prime factors of 76100 and 76114, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 76100 and 76114.

How to find the GCF of 76100 and 76114?

We will first find the prime factorization of 76100 and 76114. After we will calculate the factors of 76100 and 76114 and find the biggest common factor number .

Step-1: Prime Factorization of 76100

Prime factors of 76100 are 2, 5, 761. Prime factorization of 76100 in exponential form is:

76100 = 2² × 5² × 761¹

Step-2: Prime Factorization of 76114

Prime factors of 76114 are 2, 19, 2003. Prime factorization of 76114 in exponential form is:

76114 = 2¹ × 19¹ × 2003¹

Step-3: Factors of 76100

List of positive integer factors of 76100 that divides 76100 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 100, 761, 1522, 3044, 3805, 7610, 15220, 19025, 38050

Step-4: Factors of 76114

List of positive integer factors of 76114 that divides 76100 without a remainder.

1, 2, 19, 38, 2003, 4006, 38057

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 76100 and 76114. The biggest common factor number is the GCF number.
So the greatest common factor 76100 and 76114 is 2.

Also check out the Least Common Multiple of 76100 and 76114