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Find the Largest Number Which Divides 438 and 606 Leaving Remainder 6 in Each Case. - Mathematics

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

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Solution

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 = 24 × 33
600 = 23 × 3 × 52
HCF = product of smallest power of each common prime factor in the numbers = 23 × 3 = 24
Thus, the largest number which divides 438 and 606, leaving remainder 6 is 24.

Concept: Euclid’s Division Lemma
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