What is the Greatest Common Factor of 38640 and 38658?

Greatest common factor (GCF) of 38640 and 38658 is 6.

GCF(38640,38658) = 6

We will now calculate the prime factors of 38640 and 38658, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38640 and 38658.

How to find the GCF of 38640 and 38658?

We will first find the prime factorization of 38640 and 38658. After we will calculate the factors of 38640 and 38658 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 38658

Prime factors of 38658 are 2, 3, 17, 379. Prime factorization of 38658 in exponential form is:

38658 = 2¹ × 3¹ × 17¹ × 379¹

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 38658

List of positive integer factors of 38658 that divides 38640 without a remainder.

1, 2, 3, 6, 17, 34, 51, 102, 379, 758, 1137, 2274, 6443, 12886, 19329

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38640 and 38658. The biggest common factor number is the GCF number.
So the greatest common factor 38640 and 38658 is 6.

Also check out the Least Common Multiple of 38640 and 38658