Prime Time - Divisibility Tests

Check if the number $7248$ is divisible by $4$ and $8$.

For divisibility by $4$: Last two digits are $48$. Since $48 = 4 \times 12$, it is divisible by $4$. For divisibility by $8$: Last three digits are $248$. Since $248 = 8 \times 31$, it is divisible by $8$.

To check divisibility by $4$, we look at the last two digits. To check divisibility by $8$, we look at the last three digits.

Determine if $1331$ is divisible by $11$.

$\text{Digits at odd places (from right): } 1, 3 \Rightarrow \text{Sum} = 1 + 3 = 4$ $\text{Digits at even places (from right): } 3, 1 \Rightarrow \text{Sum} = 3 + 1 = 4$ $\text{Difference} = |4 - 4| = 0$

Since the difference between the sum of digits at odd places and even places is $0$, the number $1331$ is divisible by $11$.

Is the number $927$ divisible by $3$ and $9$?

$\text{Sum of digits} = 9 + 2 + 7 = 18$ Since $18$ is a multiple of $3$ ($3 \times 6 = 18$), it is divisible by $3$. Since $18$ is a multiple of $9$ ($9 \times 2 = 18$), it is also divisible by $9$.

If the sum of digits is divisible by $3$, the number is divisible by $3$. If the sum is divisible by $9$, the number is divisible by $9$.

Check the divisibility of $432$ by $6$.

1. Last digit is $2$, which is even. So, $432$ is divisible by $2$.
2. Sum of digits: $4 + 3 + 2 = 9$. Since $9$ is divisible by $3$, $432$ is divisible by $3$.

Because $432$ is divisible by both $2$ and $3$, it is divisible by $6$.