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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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