Find the largest number which divides 438 and 606, leaving remain… - Vidyadip

Question

Find the largest number which divides $438$ and $606$, leaving remainder $6$ in each case.

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Answer

Largest number which divides 438 and 606 , leaving remainder 6 is actually the largest number which divides $438-6=432$ and $606-6=600$, leaving remainder 0 .
Therefore, HCF of 432 and 600 gives the largest number.
Now, prime factors of 432 and 600 are:
$432 = 2^4 \times 3^3$
$600 = 2^3\times 3 \times 5^2$
HCF = product of smallest power of each common prime factor in the numbers $= 2^3\times 3 = 24$
Thus, the largest number which divides 438 and 606, leaving remainder 6 is 24.

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