What is the Greatest Common Factor of 45730 and 45750?

Greatest common factor (GCF) of 45730 and 45750 is 10.

GCF(45730,45750) = 10

We will now calculate the prime factors of 45730 and 45750, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 45730 and 45750.

How to find the GCF of 45730 and 45750?

We will first find the prime factorization of 45730 and 45750. After we will calculate the factors of 45730 and 45750 and find the biggest common factor number .

Step-1: Prime Factorization of 45730

Prime factors of 45730 are 2, 5, 17, 269. Prime factorization of 45730 in exponential form is:

45730 = 2¹ × 5¹ × 17¹ × 269¹

Step-2: 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-3: Factors of 45730

List of positive integer factors of 45730 that divides 45730 without a remainder.

1, 2, 5, 10, 17, 34, 85, 170, 269, 538, 1345, 2690, 4573, 9146, 22865

Step-4: Factors of 45750

List of positive integer factors of 45750 that divides 45730 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 45730 and 45750. The biggest common factor number is the GCF number.
So the greatest common factor 45730 and 45750 is 10.

Also check out the Least Common Multiple of 45730 and 45750