What is the Greatest Common Factor of 48960 and 48975?

Greatest common factor (GCF) of 48960 and 48975 is 15.

GCF(48960,48975) = 15

We will now calculate the prime factors of 48960 and 48975, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 48960 and 48975.

How to find the GCF of 48960 and 48975?

We will first find the prime factorization of 48960 and 48975. After we will calculate the factors of 48960 and 48975 and find the biggest common factor number .

Step-1: Prime Factorization of 48960

Prime factors of 48960 are 2, 3, 5, 17. Prime factorization of 48960 in exponential form is:

48960 = 2⁶ × 3² × 5¹ × 17¹

Step-2: Prime Factorization of 48975

Prime factors of 48975 are 3, 5, 653. Prime factorization of 48975 in exponential form is:

48975 = 3¹ × 5² × 653¹

Step-3: Factors of 48960

List of positive integer factors of 48960 that divides 48960 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 17, 18, 20, 24, 30, 32, 34, 36, 40, 45, 48, 51, 60, 64, 68, 72, 80, 85, 90, 96, 102, 120, 136, 144, 153, 160, 170, 180, 192, 204, 240, 255, 272, 288, 306, 320, 340, 360, 408, 480, 510, 544, 576, 612, 680, 720, 765, 816, 960, 1020, 1088, 1224, 1360, 1440, 1530, 1632, 2040, 2448, 2720, 2880, 3060, 3264, 4080, 4896, 5440, 6120, 8160, 9792, 12240, 16320, 24480

Step-4: Factors of 48975

List of positive integer factors of 48975 that divides 48960 without a remainder.

1, 3, 5, 15, 25, 75, 653, 1959, 3265, 9795, 16325

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 48960 and 48975. The biggest common factor number is the GCF number.
So the greatest common factor 48960 and 48975 is 15.

Also check out the Least Common Multiple of 48960 and 48975