Is the number $52563744$ divisible by $24$?

### Concept & Logic To check the divisibility of a large number by a composite number (like $24$), break the divisor into co-prime factors. Two numbers are co-prime if their highest common factor (HCF) is $1$. $$ 24 = 3 \times 8 $$ ### Step-by-Step Solution **Given:** The number is $52563744$. We need to verify its divisibility by $24$. **Calculation:** Step 1: Verify divisibility by $3$. Sum of digits = $5 + 2 + 5 + 6 + 3 + 7 + 4 + 4 = 36$. Since $36$ is divisible by $3$, the number is divisible by $3$. Step 2: Verify divisibility by $8$. Check the last three digits: $744$. $744 / 8 = 93$. Since $744$ is divisible by $8$, the entire number is divisible by $8$. Step 3: Conclusion. Since $52563744$ is divisible by both $3$ and $8$ (which are co-prime), it is divisible by their product, $24$. ### Exam Strategy & Shortcut Always select co-prime pairs for this rule. Once established, use the digital sum rule for $3$ (crossing out $3$s, $6$s, and $9$s to speed it up) and the last-three-digits rule for $8$. ### Common Pitfall The most dangerous trap is splitting $24$ into factors that are not co-prime, such as $4$ and $6$. A number can be divisible by both $4$ and $6$ but not divisible by $24$ (for example, $12$). Factors must have an HCF of $1$. ### Final Answer Therefore, the correct answer is **Yes, because it is divisible by both 3 and 8**.