What is the Greatest Common Factor of 67344 and 67360?

Greatest common factor (GCF) of 67344 and 67360 is 16.

GCF(67344,67360) = 16

We will now calculate the prime factors of 67344 and 67360, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 67344 and 67360.

How to find the GCF of 67344 and 67360?

We will first find the prime factorization of 67344 and 67360. After we will calculate the factors of 67344 and 67360 and find the biggest common factor number .

Step-1: Prime Factorization of 67344

Prime factors of 67344 are 2, 3, 23, 61. Prime factorization of 67344 in exponential form is:

67344 = 2⁴ × 3¹ × 23¹ × 61¹

Step-2: Prime Factorization of 67360

Prime factors of 67360 are 2, 5, 421. Prime factorization of 67360 in exponential form is:

67360 = 2⁵ × 5¹ × 421¹

Step-3: Factors of 67344

List of positive integer factors of 67344 that divides 67344 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 23, 24, 46, 48, 61, 69, 92, 122, 138, 183, 184, 244, 276, 366, 368, 488, 552, 732, 976, 1104, 1403, 1464, 2806, 2928, 4209, 5612, 8418, 11224, 16836, 22448, 33672

Step-4: Factors of 67360

List of positive integer factors of 67360 that divides 67344 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160, 421, 842, 1684, 2105, 3368, 4210, 6736, 8420, 13472, 16840, 33680

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 67344 and 67360. The biggest common factor number is the GCF number.
So the greatest common factor 67344 and 67360 is 16.

Also check out the Least Common Multiple of 67344 and 67360