ajv wrote:
maybe a dumb question: The largest positive integer that must divide x, means for lowest value of x which satisfies the given statement in the stem -- why?
Why is it not the largest value of x. For example, if x = 100 why cant x be 100 which will divide 100 and is the largest positive integer. What am I missing?
We can say that the largest divisor of a number is its least value (the least value of a prime number:2 and it's largest divisor is 2 only, but we can't say the maximum value part for such number which can change. The number has to be fixed to know it's divisor)
In question the least value Of X^2 is 64 (because 32,16,8,4,2 are either not divisible by 32 or is not a perfect square)
That's why the least value of X is 8. Now 8 is divisible by 4 factors (1, 2,4&8) where 8 is maximum.
It's not the largest value of X for which we want the divisor because the largest value of x^2 can extend to infinity which won't have a single value.
In your example 100 is divisible by 100 but the 100 must be because of some constraint. Let say x^2 is divisible by 1000 so x^2 has to be a multiple of 1000, we also know x^2 is a perfect square while 1000 is not that's why we will multiply 1000 with 10
Giving 10,000 as perfect square = X^2
And X = 100
Whose maximum divisor is 100.
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