What is the Greatest Common Factor of 45742 and 45760?

Greatest common factor (GCF) of 45742 and 45760 is 2.

GCF(45742,45760) = 2

We will now calculate the prime factors of 45742 and 45760, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 45742 and 45760.

How to find the GCF of 45742 and 45760?

We will first find the prime factorization of 45742 and 45760. After we will calculate the factors of 45742 and 45760 and find the biggest common factor number .

Step-1: Prime Factorization of 45742

Prime factors of 45742 are 2, 22871. Prime factorization of 45742 in exponential form is:

45742 = 2¹ × 22871¹

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 45742

List of positive integer factors of 45742 that divides 45742 without a remainder.

1, 2, 22871

Step-4: Factors of 45760

List of positive integer factors of 45760 that divides 45742 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 45742 and 45760. The biggest common factor number is the GCF number.
So the greatest common factor 45742 and 45760 is 2.

Also check out the Least Common Multiple of 45742 and 45760