What is the Greatest Common Factor of 39854 and 39872?

Greatest common factor (GCF) of 39854 and 39872 is 2.

GCF(39854,39872) = 2

We will now calculate the prime factors of 39854 and 39872, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39854 and 39872.

How to find the GCF of 39854 and 39872?

We will first find the prime factorization of 39854 and 39872. After we will calculate the factors of 39854 and 39872 and find the biggest common factor number .

Step-1: Prime Factorization of 39854

Prime factors of 39854 are 2, 19927. Prime factorization of 39854 in exponential form is:

39854 = 2¹ × 19927¹

Step-2: Prime Factorization of 39872

Prime factors of 39872 are 2, 7, 89. Prime factorization of 39872 in exponential form is:

39872 = 2⁶ × 7¹ × 89¹

Step-3: Factors of 39854

List of positive integer factors of 39854 that divides 39854 without a remainder.

1, 2, 19927

Step-4: Factors of 39872

List of positive integer factors of 39872 that divides 39854 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 32, 56, 64, 89, 112, 178, 224, 356, 448, 623, 712, 1246, 1424, 2492, 2848, 4984, 5696, 9968, 19936

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 39854 and 39872. The biggest common factor number is the GCF number.
So the greatest common factor 39854 and 39872 is 2.

Also check out the Least Common Multiple of 39854 and 39872