What is the Greatest Common Factor of 47760 and 47775?

Greatest common factor (GCF) of 47760 and 47775 is 15.

GCF(47760,47775) = 15

We will now calculate the prime factors of 47760 and 47775, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 47760 and 47775.

How to find the GCF of 47760 and 47775?

We will first find the prime factorization of 47760 and 47775. After we will calculate the factors of 47760 and 47775 and find the biggest common factor number .

Step-1: Prime Factorization of 47760

Prime factors of 47760 are 2, 3, 5, 199. Prime factorization of 47760 in exponential form is:

47760 = 2⁴ × 3¹ × 5¹ × 199¹

Step-2: Prime Factorization of 47775

Prime factors of 47775 are 3, 5, 7, 13. Prime factorization of 47775 in exponential form is:

47775 = 3¹ × 5² × 7² × 13¹

Step-3: Factors of 47760

List of positive integer factors of 47760 that divides 47760 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 199, 240, 398, 597, 796, 995, 1194, 1592, 1990, 2388, 2985, 3184, 3980, 4776, 5970, 7960, 9552, 11940, 15920, 23880

Step-4: Factors of 47775

List of positive integer factors of 47775 that divides 47760 without a remainder.

1, 3, 5, 7, 13, 15, 21, 25, 35, 39, 49, 65, 75, 91, 105, 147, 175, 195, 245, 273, 325, 455, 525, 637, 735, 975, 1225, 1365, 1911, 2275, 3185, 3675, 6825, 9555, 15925

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 47760 and 47775. The biggest common factor number is the GCF number.
So the greatest common factor 47760 and 47775 is 15.

Also check out the Least Common Multiple of 47760 and 47775