Question

# Find the largest number which divides $$615$$ and $$963$$ leaving remainder $$6$$ in each case.

Solution

## we have to  find the largest number which divide $$615$$ and $$963$$ leaving remainder $$6$$ in each case.so let us subtract $$6$$ from $$615$$ and $$963$$$$\Rightarrow$$ $$615 - 6 = 609$$$$\Rightarrow$$ $$963-6 = 957$$now lets find the $$HCF$$$$\Rightarrow$$ prime factorisation of $$609 = 29\times3\times3$$prime factorisation of $$957 = 29\times3\times11$$now lets take out the common factors from both the cases$$\Rightarrow$$ $$29$$ and $$3$$$$x = 29 \times 3 = 87$$∴ $$87$$ is the number which will divide $$615$$ and $$963$$ leaving remainder $$6$$ in each case.Maths

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