Question

Find the largest number which divides $630$ and $940$ leaving remainders $6$ and $4$.

• A. $300$
• B. $312$
• C. $42$
• D. $32$

Answer 1

The correct option is B $312$

Since on dividing $630$ by the required number, the remainder is $6$. Therefore, $630-6=624$ will be exactly divisible by the required number.

Similarly, $940-4=936$ will be also exactly divisible by the required number.

Therefore, the required number is the HCF of $624$ and $936$.

Let us do the prime factorization of $624$ and $936$ to find the HCF:

$624=2\times 2\times 2\times 2\times 3\times 13936=2\times 2\times 2\times 3\times 3\times 13\Rightarrow HCF(630,940)=2\times 2\times 2\times 3\times 13=312$

Hence, $312$ is the largest number which divides $630$ and $940$ leaving remainders $6$ and $4$.