What is the Greatest Common Factor of 83744 and 83760?

Greatest common factor (GCF) of 83744 and 83760 is 16.

GCF(83744,83760) = 16

We will now calculate the prime factors of 83744 and 83760, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 83744 and 83760.

How to find the GCF of 83744 and 83760?

We will first find the prime factorization of 83744 and 83760. After we will calculate the factors of 83744 and 83760 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 83760

Prime factors of 83760 are 2, 3, 5, 349. Prime factorization of 83760 in exponential form is:

83760 = 2⁴ × 3¹ × 5¹ × 349¹

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 83760

List of positive integer factors of 83760 that divides 83744 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240, 349, 698, 1047, 1396, 1745, 2094, 2792, 3490, 4188, 5235, 5584, 6980, 8376, 10470, 13960, 16752, 20940, 27920, 41880

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 83744 and 83760. The biggest common factor number is the GCF number.
So the greatest common factor 83744 and 83760 is 16.

Also check out the Least Common Multiple of 83744 and 83760