What is the Greatest Common Factor of 39738 and 39750?

Greatest common factor (GCF) of 39738 and 39750 is 6.

GCF(39738,39750) = 6

We will now calculate the prime factors of 39738 and 39750, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39738 and 39750.

How to find the GCF of 39738 and 39750?

We will first find the prime factorization of 39738 and 39750. After we will calculate the factors of 39738 and 39750 and find the biggest common factor number .

Step-1: Prime Factorization of 39738

Prime factors of 39738 are 2, 3, 37, 179. Prime factorization of 39738 in exponential form is:

39738 = 2¹ × 3¹ × 37¹ × 179¹

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 39738

List of positive integer factors of 39738 that divides 39738 without a remainder.

1, 2, 3, 6, 37, 74, 111, 179, 222, 358, 537, 1074, 6623, 13246, 19869

Step-4: Factors of 39750

List of positive integer factors of 39750 that divides 39738 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 39738 and 39750. The biggest common factor number is the GCF number.
So the greatest common factor 39738 and 39750 is 6.

Also check out the Least Common Multiple of 39738 and 39750