What is the Greatest Common Factor of 39500 and 39514?

Greatest common factor (GCF) of 39500 and 39514 is 2.

GCF(39500,39514) = 2

We will now calculate the prime factors of 39500 and 39514, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39500 and 39514.

How to find the GCF of 39500 and 39514?

We will first find the prime factorization of 39500 and 39514. After we will calculate the factors of 39500 and 39514 and find the biggest common factor number .

Step-1: Prime Factorization of 39500

Prime factors of 39500 are 2, 5, 79. Prime factorization of 39500 in exponential form is:

39500 = 2² × 5³ × 79¹

Step-2: Prime Factorization of 39514

Prime factors of 39514 are 2, 23, 859. Prime factorization of 39514 in exponential form is:

39514 = 2¹ × 23¹ × 859¹

Step-3: Factors of 39500

List of positive integer factors of 39500 that divides 39500 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 79, 100, 125, 158, 250, 316, 395, 500, 790, 1580, 1975, 3950, 7900, 9875, 19750

Step-4: Factors of 39514

List of positive integer factors of 39514 that divides 39500 without a remainder.

1, 2, 23, 46, 859, 1718, 19757

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39500 and 39514. The biggest common factor number is the GCF number.
So the greatest common factor 39500 and 39514 is 2.

Also check out the Least Common Multiple of 39500 and 39514