What is the Greatest Common Factor of 45750 and 45760?

Greatest common factor (GCF) of 45750 and 45760 is 10.

GCF(45750,45760) = 10

We will now calculate the prime factors of 45750 and 45760, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 45750 and 45760.

How to find the GCF of 45750 and 45760?

We will first find the prime factorization of 45750 and 45760. After we will calculate the factors of 45750 and 45760 and find the biggest common factor number .

Step-1: Prime Factorization of 45750

Prime factors of 45750 are 2, 3, 5, 61. Prime factorization of 45750 in exponential form is:

45750 = 2¹ × 3¹ × 5³ × 61¹

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 45750

List of positive integer factors of 45750 that divides 45750 without a remainder.

1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 61, 75, 122, 125, 150, 183, 250, 305, 366, 375, 610, 750, 915, 1525, 1830, 3050, 4575, 7625, 9150, 15250, 22875

Step-4: Factors of 45760

List of positive integer factors of 45760 that divides 45750 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 45750 and 45760. The biggest common factor number is the GCF number.
So the greatest common factor 45750 and 45760 is 10.

Also check out the Least Common Multiple of 45750 and 45760