What is the Greatest Common Factor of 48945 and 48960?

Greatest common factor (GCF) of 48945 and 48960 is 15.

GCF(48945,48960) = 15

We will now calculate the prime factors of 48945 and 48960, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 48945 and 48960.

How to find the GCF of 48945 and 48960?

We will first find the prime factorization of 48945 and 48960. After we will calculate the factors of 48945 and 48960 and find the biggest common factor number .

Step-1: Prime Factorization of 48945

Prime factors of 48945 are 3, 5, 13, 251. Prime factorization of 48945 in exponential form is:

48945 = 3¹ × 5¹ × 13¹ × 251¹

Step-2: 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-3: Factors of 48945

List of positive integer factors of 48945 that divides 48945 without a remainder.

1, 3, 5, 13, 15, 39, 65, 195, 251, 753, 1255, 3263, 3765, 9789, 16315

Step-4: Factors of 48960

List of positive integer factors of 48960 that divides 48945 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 48945 and 48960. The biggest common factor number is the GCF number.
So the greatest common factor 48945 and 48960 is 15.

Also check out the Least Common Multiple of 48945 and 48960