What is the Greatest Common Factor of 67824 and 67840?

Greatest common factor (GCF) of 67824 and 67840 is 16.

GCF(67824,67840) = 16

We will now calculate the prime factors of 67824 and 67840, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67824 and 67840.

How to find the GCF of 67824 and 67840?

We will first find the prime factorization of 67824 and 67840. After we will calculate the factors of 67824 and 67840 and find the biggest common factor number .

Step-1: Prime Factorization of 67824

Prime factors of 67824 are 2, 3, 157. Prime factorization of 67824 in exponential form is:

67824 = 2⁴ × 3³ × 157¹

Step-2: Prime Factorization of 67840

Prime factors of 67840 are 2, 5, 53. Prime factorization of 67840 in exponential form is:

67840 = 2⁸ × 5¹ × 53¹

Step-3: Factors of 67824

List of positive integer factors of 67824 that divides 67824 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 36, 48, 54, 72, 108, 144, 157, 216, 314, 432, 471, 628, 942, 1256, 1413, 1884, 2512, 2826, 3768, 4239, 5652, 7536, 8478, 11304, 16956, 22608, 33912

Step-4: Factors of 67840

List of positive integer factors of 67840 that divides 67824 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 53, 64, 80, 106, 128, 160, 212, 256, 265, 320, 424, 530, 640, 848, 1060, 1280, 1696, 2120, 3392, 4240, 6784, 8480, 13568, 16960, 33920

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67824 and 67840. The biggest common factor number is the GCF number.
So the greatest common factor 67824 and 67840 is 16.

Also check out the Least Common Multiple of 67824 and 67840