What is the Greatest Common Factor of 38624 and 38640?

Greatest common factor (GCF) of 38624 and 38640 is 16.

GCF(38624,38640) = 16

We will now calculate the prime factors of 38624 and 38640, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38624 and 38640.

How to find the GCF of 38624 and 38640?

We will first find the prime factorization of 38624 and 38640. After we will calculate the factors of 38624 and 38640 and find the biggest common factor number .

Step-1: Prime Factorization of 38624

Prime factors of 38624 are 2, 17, 71. Prime factorization of 38624 in exponential form is:

38624 = 2⁵ × 17¹ × 71¹

Step-2: 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-3: Factors of 38624

List of positive integer factors of 38624 that divides 38624 without a remainder.

1, 2, 4, 8, 16, 17, 32, 34, 68, 71, 136, 142, 272, 284, 544, 568, 1136, 1207, 2272, 2414, 4828, 9656, 19312

Step-4: Factors of 38640

List of positive integer factors of 38640 that divides 38624 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38624 and 38640. The biggest common factor number is the GCF number.
So the greatest common factor 38624 and 38640 is 16.

Also check out the Least Common Multiple of 38624 and 38640