What is the Greatest Common Factor of 47745 and 47760?

Greatest common factor (GCF) of 47745 and 47760 is 15.

GCF(47745,47760) = 15

We will now calculate the prime factors of 47745 and 47760, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 47745 and 47760.

How to find the GCF of 47745 and 47760?

We will first find the prime factorization of 47745 and 47760. After we will calculate the factors of 47745 and 47760 and find the biggest common factor number .

Step-1: Prime Factorization of 47745

Prime factors of 47745 are 3, 5, 1061. Prime factorization of 47745 in exponential form is:

47745 = 3² × 5¹ × 1061¹

Step-2: 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-3: Factors of 47745

List of positive integer factors of 47745 that divides 47745 without a remainder.

1, 3, 5, 9, 15, 45, 1061, 3183, 5305, 9549, 15915

Step-4: Factors of 47760

List of positive integer factors of 47760 that divides 47745 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 47745 and 47760. The biggest common factor number is the GCF number.
So the greatest common factor 47745 and 47760 is 15.

Also check out the Least Common Multiple of 47745 and 47760