What is the Greatest Common Factor of 39730 and 39750?

Greatest common factor (GCF) of 39730 and 39750 is 10.

GCF(39730,39750) = 10

We will now calculate the prime factors of 39730 and 39750, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39730 and 39750.

How to find the GCF of 39730 and 39750?

We will first find the prime factorization of 39730 and 39750. After we will calculate the factors of 39730 and 39750 and find the biggest common factor number .

Step-1: Prime Factorization of 39730

Prime factors of 39730 are 2, 5, 29, 137. Prime factorization of 39730 in exponential form is:

39730 = 2¹ × 5¹ × 29¹ × 137¹

Step-2: Prime Factorization of 39750

Prime factors of 39750 are 2, 3, 5, 53. Prime factorization of 39750 in exponential form is:

39750 = 2¹ × 3¹ × 5³ × 53¹

Step-3: Factors of 39730

List of positive integer factors of 39730 that divides 39730 without a remainder.

1, 2, 5, 10, 29, 58, 137, 145, 274, 290, 685, 1370, 3973, 7946, 19865

Step-4: Factors of 39750

List of positive integer factors of 39750 that divides 39730 without a remainder.

1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 53, 75, 106, 125, 150, 159, 250, 265, 318, 375, 530, 750, 795, 1325, 1590, 2650, 3975, 6625, 7950, 13250, 19875

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39730 and 39750. The biggest common factor number is the GCF number.
So the greatest common factor 39730 and 39750 is 10.

Also check out the Least Common Multiple of 39730 and 39750