What is the Greatest Common Factor of 35730 and 35750?

Greatest common factor (GCF) of 35730 and 35750 is 10.

GCF(35730,35750) = 10

We will now calculate the prime factors of 35730 and 35750, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 35730 and 35750.

How to find the GCF of 35730 and 35750?

We will first find the prime factorization of 35730 and 35750. After we will calculate the factors of 35730 and 35750 and find the biggest common factor number .

Step-1: Prime Factorization of 35730

Prime factors of 35730 are 2, 3, 5, 397. Prime factorization of 35730 in exponential form is:

35730 = 2¹ × 3² × 5¹ × 397¹

Step-2: Prime Factorization of 35750

Prime factors of 35750 are 2, 5, 11, 13. Prime factorization of 35750 in exponential form is:

35750 = 2¹ × 5³ × 11¹ × 13¹

Step-3: Factors of 35730

List of positive integer factors of 35730 that divides 35730 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90, 397, 794, 1191, 1985, 2382, 3573, 3970, 5955, 7146, 11910, 17865

Step-4: Factors of 35750

List of positive integer factors of 35750 that divides 35730 without a remainder.

1, 2, 5, 10, 11, 13, 22, 25, 26, 50, 55, 65, 110, 125, 130, 143, 250, 275, 286, 325, 550, 650, 715, 1375, 1430, 1625, 2750, 3250, 3575, 7150, 17875

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 35730 and 35750. The biggest common factor number is the GCF number.
So the greatest common factor 35730 and 35750 is 10.

Also check out the Least Common Multiple of 35730 and 35750