What is the Greatest Common Factor of 71730 and 71750?

Greatest common factor (GCF) of 71730 and 71750 is 10.

GCF(71730,71750) = 10

We will now calculate the prime factors of 71730 and 71750, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 71730 and 71750.

How to find the GCF of 71730 and 71750?

We will first find the prime factorization of 71730 and 71750. After we will calculate the factors of 71730 and 71750 and find the biggest common factor number .

Step-1: Prime Factorization of 71730

Prime factors of 71730 are 2, 3, 5, 797. Prime factorization of 71730 in exponential form is:

71730 = 2¹ × 3² × 5¹ × 797¹

Step-2: Prime Factorization of 71750

Prime factors of 71750 are 2, 5, 7, 41. Prime factorization of 71750 in exponential form is:

71750 = 2¹ × 5³ × 7¹ × 41¹

Step-3: Factors of 71730

List of positive integer factors of 71730 that divides 71730 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90, 797, 1594, 2391, 3985, 4782, 7173, 7970, 11955, 14346, 23910, 35865

Step-4: Factors of 71750

List of positive integer factors of 71750 that divides 71730 without a remainder.

1, 2, 5, 7, 10, 14, 25, 35, 41, 50, 70, 82, 125, 175, 205, 250, 287, 350, 410, 574, 875, 1025, 1435, 1750, 2050, 2870, 5125, 7175, 10250, 14350, 35875

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 71730 and 71750. The biggest common factor number is the GCF number.
So the greatest common factor 71730 and 71750 is 10.

Also check out the Least Common Multiple of 71730 and 71750