What is the Greatest Common Factor of 83744 and 83762?

Greatest common factor (GCF) of 83744 and 83762 is 2.

GCF(83744,83762) = 2

We will now calculate the prime factors of 83744 and 83762, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 83744 and 83762.

How to find the GCF of 83744 and 83762?

We will first find the prime factorization of 83744 and 83762. After we will calculate the factors of 83744 and 83762 and find the biggest common factor number .

Step-1: Prime Factorization of 83744

Prime factors of 83744 are 2, 2617. Prime factorization of 83744 in exponential form is:

83744 = 2⁵ × 2617¹

Step-2: Prime Factorization of 83762

Prime factors of 83762 are 2, 7, 31, 193. Prime factorization of 83762 in exponential form is:

83762 = 2¹ × 7¹ × 31¹ × 193¹

Step-3: Factors of 83744

List of positive integer factors of 83744 that divides 83744 without a remainder.

1, 2, 4, 8, 16, 32, 2617, 5234, 10468, 20936, 41872

Step-4: Factors of 83762

List of positive integer factors of 83762 that divides 83744 without a remainder.

1, 2, 7, 14, 31, 62, 193, 217, 386, 434, 1351, 2702, 5983, 11966, 41881

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 83744 and 83762. The biggest common factor number is the GCF number.
So the greatest common factor 83744 and 83762 is 2.

Also check out the Least Common Multiple of 83744 and 83762