Question

Find the largest number which on dividing 1251, 9377 and 15628 leaves remainders 1, 2 and 3 respectively.

Answer 1

Dear student,

$$\begin{gathered} numbers1251,9377and15628leaveremainder1,2and3respectively. \\ subtractingtheremaindersfromthenumbersitself, \\ i.e. \\ 1251-1=1250 \\ 9377-2=9375 \\ 15628-3=15625 \\ ThelargestnumberforthegivenconditionwillbefoundbyfindingHCF \\ ofthenumbers1250,9375and15625 \\ Primefactori\sin gthenumbers \\ 1250=2\times 5\times 5\times 5\times 5=2\times 5^4 \\ 9375=3\times 5\times 5\times 5\times 5\times 5=3\times 5^5 \\ 15625=5\times 5\times 5\times 5\times 5\times 5=5^6 \\ HCF=5^4=625 \\ Therefor625isthelargestnumberwhichondividing1251,9377and15628will \\ leaveremainder1,2and3respectively. \end{gathered}$$
Regards