Question

Find the greatest numbers that will divide $445,572$ and $699$ leaving remainders $4,5$ and $6$ respectively.

Answer 1

$445-4=441$
$572-5=567$
$699-6=693$
The greatest common factors of 441, 567 and 693 is,
$441=3\times 3\times 7\times 7$
$567=3\times 3\times 3\times 3\times 7$
$693=3\times 3\times 7\times 11$
The common factors are $3\times 3\times 7=63$.
$\frac{445}{63}=7$ with remainder as 4.
$\frac{572}{63}=9$ with remainder as 5.
$\frac{699}{63}=11$ with remainder as 6.
Therefore, 63 is the greatest number.