Question 130

If r is the remainder 2013 when each of 6454, 7306 and 8797is divided by the greatest number d(d > 1), then (d—r) is equal to:

Solution

Let the numbers are $$6454-r, 7306-r, 8797$$

Hence, the HCF of the number $$(7306-6454),(8797-7306), (8797-6454)$$

$$852=2\times 2\times 3\times 71$$

$$1491=3\times 71\times 7$$

$$2343=3\times 71\times 11$$

Hence, the HCF$$ d=3\times 71=213$$

Now, $$213\times 3+64$$

So, r=64, Hence, the required number $$=d-r=213-64=149$$.

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