What is the Greatest Common Factor of 38640 and 38655?

Greatest common factor (GCF) of 38640 and 38655 is 15.

GCF(38640,38655) = 15

We will now calculate the prime factors of 38640 and 38655, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38640 and 38655.

How to find the GCF of 38640 and 38655?

We will first find the prime factorization of 38640 and 38655. After we will calculate the factors of 38640 and 38655 and find the biggest common factor number .

Step-1: Prime Factorization of 38640

Prime factors of 38640 are 2, 3, 5, 7, 23. Prime factorization of 38640 in exponential form is:

38640 = 2⁴ × 3¹ × 5¹ × 7¹ × 23¹

Step-2: Prime Factorization of 38655

Prime factors of 38655 are 3, 5, 859. Prime factorization of 38655 in exponential form is:

38655 = 3² × 5¹ × 859¹

Step-3: Factors of 38640

List of positive integer factors of 38640 that divides 38640 without a remainder.

1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 23, 24, 28, 30, 35, 40, 42, 46, 48, 56, 60, 69, 70, 80, 84, 92, 105, 112, 115, 120, 138, 140, 161, 168, 184, 210, 230, 240, 276, 280, 322, 336, 345, 368, 420, 460, 483, 552, 560, 644, 690, 805, 840, 920, 966, 1104, 1288, 1380, 1610, 1680, 1840, 1932, 2415, 2576, 2760, 3220, 3864, 4830, 5520, 6440, 7728, 9660, 12880, 19320

Step-4: Factors of 38655

List of positive integer factors of 38655 that divides 38640 without a remainder.

1, 3, 5, 9, 15, 45, 859, 2577, 4295, 7731, 12885

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38640 and 38655. The biggest common factor number is the GCF number.
So the greatest common factor 38640 and 38655 is 15.

Also check out the Least Common Multiple of 38640 and 38655