What is the Greatest Common Factor of 38640 and 38646?

Greatest common factor (GCF) of 38640 and 38646 is 6.

GCF(38640,38646) = 6

We will now calculate the prime factors of 38640 and 38646, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38640 and 38646.

How to find the GCF of 38640 and 38646?

We will first find the prime factorization of 38640 and 38646. After we will calculate the factors of 38640 and 38646 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 38646

Prime factors of 38646 are 2, 3, 19, 113. Prime factorization of 38646 in exponential form is:

38646 = 2¹ × 3² × 19¹ × 113¹

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 38646

List of positive integer factors of 38646 that divides 38640 without a remainder.

1, 2, 3, 6, 9, 18, 19, 38, 57, 113, 114, 171, 226, 339, 342, 678, 1017, 2034, 2147, 4294, 6441, 12882, 19323

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38640 and 38646. The biggest common factor number is the GCF number.
So the greatest common factor 38640 and 38646 is 6.

Also check out the Least Common Multiple of 38640 and 38646