What is the greatest common factor of 24, 8, and 16?

Answer 1

To find the greatest common factor (GCF) of the numbers 24, 8, and 16, we start by determining the prime factorization of each number:

• 24:

  • \(24 = 2^3 \times 3^1\)

• 8:

  • \(8 = 2^3\)

• 16:

  • \(16 = 2^4\)

Next, we identify the common prime factors and their lowest powers:

• The only common prime factor among the three numbers is \(2\).
• The lowest exponent of \(2\) in all factorizations is \(2^3\).

Now we find the GCF: \[ GCF = 2^3 = 8 \]

Therefore, the greatest common factor of 24, 8, and 16 is \(\boxed{8}\).