What is the Greatest Common Factor of 67809 and 67824?

Greatest common factor (GCF) of 67809 and 67824 is 3.

GCF(67809,67824) = 3

We will now calculate the prime factors of 67809 and 67824, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67809 and 67824.

How to find the GCF of 67809 and 67824?

We will first find the prime factorization of 67809 and 67824. After we will calculate the factors of 67809 and 67824 and find the biggest common factor number .

Step-1: Prime Factorization of 67809

Prime factors of 67809 are 3, 7, 3229. Prime factorization of 67809 in exponential form is:

67809 = 3¹ × 7¹ × 3229¹

Step-2: 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-3: Factors of 67809

List of positive integer factors of 67809 that divides 67809 without a remainder.

1, 3, 7, 21, 3229, 9687, 22603

Step-4: Factors of 67824

List of positive integer factors of 67824 that divides 67809 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67809 and 67824. The biggest common factor number is the GCF number.
So the greatest common factor 67809 and 67824 is 3.

Also check out the Least Common Multiple of 67809 and 67824