What is the Greatest Common Factor of 39872 and 39888?

Greatest common factor (GCF) of 39872 and 39888 is 16.

GCF(39872,39888) = 16

We will now calculate the prime factors of 39872 and 39888, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 39872 and 39888.

How to find the GCF of 39872 and 39888?

We will first find the prime factorization of 39872 and 39888. After we will calculate the factors of 39872 and 39888 and find the biggest common factor number .

Step-1: 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-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 39872

List of positive integer factors of 39872 that divides 39872 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

Step-4: Factors of 39888

List of positive integer factors of 39888 that divides 39872 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 39872 and 39888. The biggest common factor number is the GCF number.
So the greatest common factor 39872 and 39888 is 16.

Also check out the Least Common Multiple of 39872 and 39888