What is the Greatest Common Factor of 75675 and 75680?

Greatest common factor (GCF) of 75675 and 75680 is 5.

GCF(75675,75680) = 5

We will now calculate the prime factors of 75675 and 75680, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75675 and 75680.

How to find the GCF of 75675 and 75680?

We will first find the prime factorization of 75675 and 75680. After we will calculate the factors of 75675 and 75680 and find the biggest common factor number .

Step-1: Prime Factorization of 75675

Prime factors of 75675 are 3, 5, 1009. Prime factorization of 75675 in exponential form is:

75675 = 3¹ × 5² × 1009¹

Step-2: Prime Factorization of 75680

Prime factors of 75680 are 2, 5, 11, 43. Prime factorization of 75680 in exponential form is:

75680 = 2⁵ × 5¹ × 11¹ × 43¹

Step-3: Factors of 75675

List of positive integer factors of 75675 that divides 75675 without a remainder.

1, 3, 5, 15, 25, 75, 1009, 3027, 5045, 15135, 25225

Step-4: Factors of 75680

List of positive integer factors of 75680 that divides 75675 without a remainder.

1, 2, 4, 5, 8, 10, 11, 16, 20, 22, 32, 40, 43, 44, 55, 80, 86, 88, 110, 160, 172, 176, 215, 220, 344, 352, 430, 440, 473, 688, 860, 880, 946, 1376, 1720, 1760, 1892, 2365, 3440, 3784, 4730, 6880, 7568, 9460, 15136, 18920, 37840

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75675 and 75680. The biggest common factor number is the GCF number.
So the greatest common factor 75675 and 75680 is 5.

Also check out the Least Common Multiple of 75675 and 75680