What is the Greatest Common Factor of 39750 and 39762?

Greatest common factor (GCF) of 39750 and 39762 is 6.

GCF(39750,39762) = 6

We will now calculate the prime factors of 39750 and 39762, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39750 and 39762.

How to find the GCF of 39750 and 39762?

We will first find the prime factorization of 39750 and 39762. After we will calculate the factors of 39750 and 39762 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 39762

Prime factors of 39762 are 2, 3, 47. Prime factorization of 39762 in exponential form is:

39762 = 2¹ × 3² × 47²

Step-3: Factors of 39750

List of positive integer factors of 39750 that divides 39750 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

Step-4: Factors of 39762

List of positive integer factors of 39762 that divides 39750 without a remainder.

1, 2, 3, 6, 9, 18, 47, 94, 141, 282, 423, 846, 2209, 4418, 6627, 13254, 19881

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39750 and 39762. The biggest common factor number is the GCF number.
So the greatest common factor 39750 and 39762 is 6.

Also check out the Least Common Multiple of 39750 and 39762