What is the Greatest Common Factor of 38976 and 38985?

Greatest common factor (GCF) of 38976 and 38985 is 3.

GCF(38976,38985) = 3

We will now calculate the prime factors of 38976 and 38985, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38976 and 38985.

How to find the GCF of 38976 and 38985?

We will first find the prime factorization of 38976 and 38985. After we will calculate the factors of 38976 and 38985 and find the biggest common factor number .

Step-1: Prime Factorization of 38976

Prime factors of 38976 are 2, 3, 7, 29. Prime factorization of 38976 in exponential form is:

38976 = 2⁶ × 3¹ × 7¹ × 29¹

Step-2: Prime Factorization of 38985

Prime factors of 38985 are 3, 5, 23, 113. Prime factorization of 38985 in exponential form is:

38985 = 3¹ × 5¹ × 23¹ × 113¹

Step-3: Factors of 38976

List of positive integer factors of 38976 that divides 38976 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 29, 32, 42, 48, 56, 58, 64, 84, 87, 96, 112, 116, 168, 174, 192, 203, 224, 232, 336, 348, 406, 448, 464, 609, 672, 696, 812, 928, 1218, 1344, 1392, 1624, 1856, 2436, 2784, 3248, 4872, 5568, 6496, 9744, 12992, 19488

Step-4: Factors of 38985

List of positive integer factors of 38985 that divides 38976 without a remainder.

1, 3, 5, 15, 23, 69, 113, 115, 339, 345, 565, 1695, 2599, 7797, 12995

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38976 and 38985. The biggest common factor number is the GCF number.
So the greatest common factor 38976 and 38985 is 3.

Also check out the Least Common Multiple of 38976 and 38985