Question

Find the greatest number that will divide $445,572and699$ leaving remainders $4,56$ respectively.

• A. $64$
• B. $63$
• C. $44$
• D. $21$

Answer 1

The correct option is B $63$

$445-4=441$

$572-5=567$

$699-6=693$

$\Rightarrow$ Now, we have to find common factors of $441,567$ and $693$

$441=3\times 3\times 7\times 7$

$572=3\times 3\times 3\times 3\times 7$

$693=3\times 3\times 7\times 11$

$\Rightarrow$ The common factors $=3\times 3\times 7=63$

$\Rightarrow$ Here, we can see after dividing $445,572,699$ by $63$ we get remainder $4,5,6$.

$\therefore$ The greatest number that will divide $445,572$ and $699$ leaving remainders $4,5,6$ is $63$