What is the Greatest Common Factor of 35744 and 35760?

Greatest common factor (GCF) of 35744 and 35760 is 16.

GCF(35744,35760) = 16

We will now calculate the prime factors of 35744 and 35760, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35744 and 35760.

How to find the GCF of 35744 and 35760?

We will first find the prime factorization of 35744 and 35760. After we will calculate the factors of 35744 and 35760 and find the biggest common factor number .

Step-1: Prime Factorization of 35744

Prime factors of 35744 are 2, 1117. Prime factorization of 35744 in exponential form is:

35744 = 2⁵ × 1117¹

Step-2: Prime Factorization of 35760

Prime factors of 35760 are 2, 3, 5, 149. Prime factorization of 35760 in exponential form is:

35760 = 2⁴ × 3¹ × 5¹ × 149¹

Step-3: Factors of 35744

List of positive integer factors of 35744 that divides 35744 without a remainder.

1, 2, 4, 8, 16, 32, 1117, 2234, 4468, 8936, 17872

Step-4: Factors of 35760

List of positive integer factors of 35760 that divides 35744 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 149, 240, 298, 447, 596, 745, 894, 1192, 1490, 1788, 2235, 2384, 2980, 3576, 4470, 5960, 7152, 8940, 11920, 17880

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35744 and 35760. The biggest common factor number is the GCF number.
So the greatest common factor 35744 and 35760 is 16.

Also check out the Least Common Multiple of 35744 and 35760