What is the Greatest Common Factor of 38640 and 38660?

Greatest common factor (GCF) of 38640 and 38660 is 20.

GCF(38640,38660) = 20

We will now calculate the prime factors of 38640 and 38660, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38640 and 38660.

How to find the GCF of 38640 and 38660?

We will first find the prime factorization of 38640 and 38660. After we will calculate the factors of 38640 and 38660 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 38660

Prime factors of 38660 are 2, 5, 1933. Prime factorization of 38660 in exponential form is:

38660 = 2² × 5¹ × 1933¹

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 38660

List of positive integer factors of 38660 that divides 38640 without a remainder.

1, 2, 4, 5, 10, 20, 1933, 3866, 7732, 9665, 19330

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38640 and 38660. The biggest common factor number is the GCF number.
So the greatest common factor 38640 and 38660 is 20.

Also check out the Least Common Multiple of 38640 and 38660