What is the Greatest Common Factor of 75344 and 75360?

Greatest common factor (GCF) of 75344 and 75360 is 16.

GCF(75344,75360) = 16

We will now calculate the prime factors of 75344 and 75360, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75344 and 75360.

How to find the GCF of 75344 and 75360?

We will first find the prime factorization of 75344 and 75360. After we will calculate the factors of 75344 and 75360 and find the biggest common factor number .

Step-1: Prime Factorization of 75344

Prime factors of 75344 are 2, 17, 277. Prime factorization of 75344 in exponential form is:

75344 = 2⁴ × 17¹ × 277¹

Step-2: Prime Factorization of 75360

Prime factors of 75360 are 2, 3, 5, 157. Prime factorization of 75360 in exponential form is:

75360 = 2⁵ × 3¹ × 5¹ × 157¹

Step-3: Factors of 75344

List of positive integer factors of 75344 that divides 75344 without a remainder.

1, 2, 4, 8, 16, 17, 34, 68, 136, 272, 277, 554, 1108, 2216, 4432, 4709, 9418, 18836, 37672

Step-4: Factors of 75360

List of positive integer factors of 75360 that divides 75344 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 80, 96, 120, 157, 160, 240, 314, 471, 480, 628, 785, 942, 1256, 1570, 1884, 2355, 2512, 3140, 3768, 4710, 5024, 6280, 7536, 9420, 12560, 15072, 18840, 25120, 37680

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75344 and 75360. The biggest common factor number is the GCF number.
So the greatest common factor 75344 and 75360 is 16.

Also check out the Least Common Multiple of 75344 and 75360