What is the Greatest Common Factor of 45744 and 45760?

Greatest common factor (GCF) of 45744 and 45760 is 16.

GCF(45744,45760) = 16

We will now calculate the prime factors of 45744 and 45760, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 45744 and 45760.

How to find the GCF of 45744 and 45760?

We will first find the prime factorization of 45744 and 45760. After we will calculate the factors of 45744 and 45760 and find the biggest common factor number .

Step-1: Prime Factorization of 45744

Prime factors of 45744 are 2, 3, 953. Prime factorization of 45744 in exponential form is:

45744 = 2⁴ × 3¹ × 953¹

Step-2: Prime Factorization of 45760

Prime factors of 45760 are 2, 5, 11, 13. Prime factorization of 45760 in exponential form is:

45760 = 2⁶ × 5¹ × 11¹ × 13¹

Step-3: Factors of 45744

List of positive integer factors of 45744 that divides 45744 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 953, 1906, 2859, 3812, 5718, 7624, 11436, 15248, 22872

Step-4: Factors of 45760

List of positive integer factors of 45760 that divides 45744 without a remainder.

1, 2, 4, 5, 8, 10, 11, 13, 16, 20, 22, 26, 32, 40, 44, 52, 55, 64, 65, 80, 88, 104, 110, 130, 143, 160, 176, 208, 220, 260, 286, 320, 352, 416, 440, 520, 572, 704, 715, 832, 880, 1040, 1144, 1430, 1760, 2080, 2288, 2860, 3520, 4160, 4576, 5720, 9152, 11440, 22880

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 45744 and 45760. The biggest common factor number is the GCF number.
So the greatest common factor 45744 and 45760 is 16.

Also check out the Least Common Multiple of 45744 and 45760