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Mathematics · 2026 · 3 marks
CBSE 2026 · Region 4 · Set 3 · Q28
Find the greatest number which divides 764 and 1198, leaving remainders 8 and 10 respectively.
Find the greatest number which divides $\displaystyle 764$ and $\displaystyle 1198$, leaving remainders $\displaystyle 8$ and $\displaystyle 10$ respectively.
Marking-scheme solution
\(\displaystyle 764-8=756\) and \(\displaystyle 1198-10=1188\)
\(\displaystyle 756=2^{2} \times 3^{3} \times 7\)
\(\displaystyle 1188=2^{2} \times 3^{3} \times 11\)
H.C.F. \(\displaystyle (756,1188)=2^{2} \times 3^{3}=108\)
∴ Required greatest number is 108.
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