If both 52 and 33 are factors of n x (25) (62) (73), then what is the smallest possible positive value of n?
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Step-by-step explanation:
In order to be divisible by 25 and 9, x must have those factors. We can see that 6^2 can satisfy the 3^2 factor but there are no factors which can actually satisfy 5^2 to be its factor.
Hence 25 is the smallest positive number possible for n so that 25 and 9 can still be the factor of x.
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Answer:
Step-by-step explanation:
(25)∗(62)∗(73)∗n(25)∗(62)∗(73)∗n is the given number.
If both 5^2 & 3^3 are factors, then they must be present in the number.
Leaving rest of the prime factors and splitting 6^2 into 3^2 * 2^3.
The number is lacking 5^2 & a 3, so that 5^2 and 3^3 is a factor.
Hence the smallest number is 5^2 * 3 = 75
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