What is the Greatest Common Factor of 67824 and 67842?

Greatest common factor (GCF) of 67824 and 67842 is 18.

GCF(67824,67842) = 18

We will now calculate the prime factors of 67824 and 67842, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67824 and 67842.

How to find the GCF of 67824 and 67842?

We will first find the prime factorization of 67824 and 67842. After we will calculate the factors of 67824 and 67842 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 67842

Prime factors of 67842 are 2, 3, 3769. Prime factorization of 67842 in exponential form is:

67842 = 2¹ × 3² × 3769¹

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 67842

List of positive integer factors of 67842 that divides 67824 without a remainder.

1, 2, 3, 6, 9, 18, 3769, 7538, 11307, 22614, 33921

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67824 and 67842. The biggest common factor number is the GCF number.
So the greatest common factor 67824 and 67842 is 18.

Also check out the Least Common Multiple of 67824 and 67842