What is the Greatest Common Factor of 39874 and 39888?

Greatest common factor (GCF) of 39874 and 39888 is 2.

GCF(39874,39888) = 2

We will now calculate the prime factors of 39874 and 39888, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39874 and 39888.

How to find the GCF of 39874 and 39888?

We will first find the prime factorization of 39874 and 39888. After we will calculate the factors of 39874 and 39888 and find the biggest common factor number .

Step-1: Prime Factorization of 39874

Prime factors of 39874 are 2, 19937. Prime factorization of 39874 in exponential form is:

39874 = 2¹ × 19937¹

Step-2: Prime Factorization of 39888

Prime factors of 39888 are 2, 3, 277. Prime factorization of 39888 in exponential form is:

39888 = 2⁴ × 3² × 277¹

Step-3: Factors of 39874

List of positive integer factors of 39874 that divides 39874 without a remainder.

1, 2, 19937

Step-4: Factors of 39888

List of positive integer factors of 39888 that divides 39874 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144, 277, 554, 831, 1108, 1662, 2216, 2493, 3324, 4432, 4986, 6648, 9972, 13296, 19944

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39874 and 39888. The biggest common factor number is the GCF number.
So the greatest common factor 39874 and 39888 is 2.

Also check out the Least Common Multiple of 39874 and 39888