Perform prime factorization

Break down each number into its prime factors: $16 = 2 \times 2 \times 2 \times 2 = 2^4$, $20 = 2 \times 2 \times 5 = 2^2 \times 5^1$, and $24 = 2 \times 2 \times 2 \times 3 = 2^3 \times 3^1$.

$16=2^4, 20=2^2 \times 5, 24=2^3 \times 3$

Identify common prime factors

The only prime factor common to all three numbers is 2. Select the factor with the lowest exponent present in the factorizations, which is $2^2$.

$HCF = 2^2 = 4$

Verify result

Since 4 is the largest integer that divides 16, 20, and 24 without leaving a remainder, the HCF is 4.

$4 \times 4=16, 4 \times 5=20, 4 \times 6=24$