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17 Sep 2013, 01:16
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78% (02:02) correct
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An integer n that is greater than 1 is said to be "prime-saturated" if it has no prime factor greater than or equal to \(\sqrt{n}\). Which of the following integers is prime saturated?
A) 6
B) 35
C) 46
D) 66
E) 75
Can someone explain the answer choices. Thanks!
A) 6
B) 35
C) 46
D) 66
E) 75
Can someone explain the answer choices. Thanks!
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17 Sep 2013, 01:34
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An integer n that is greater than 1 is said to be "prime-saturated" if it has no prime factor greater than or equal to \(\sqrt{n}\). Which of the following integers is prime saturated?
A. 6
B. 35
C. 46
D. 66
E. 75
According to the definition integer is said to be "prime-saturated" if the square of its largest prime is smaller than the integer itself.
Only E satisfies this: 75=3*5^2 --> the largest prime is 5 --> 5^2=25<75.
Answer: E.
Similar question to practice: a-number-is-said-to-be-prime-saturated-106511.html
Hope it helps.
A. 6
B. 35
C. 46
D. 66
E. 75
According to the definition integer is said to be "prime-saturated" if the square of its largest prime is smaller than the integer itself.
Only E satisfies this: 75=3*5^2 --> the largest prime is 5 --> 5^2=25<75.
Answer: E.
Similar question to practice: a-number-is-said-to-be-prime-saturated-106511.html
Hope it helps.
30 Jan 2018, 08:35
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fozzzy
So, n is prime saturated if the largest prime factor of n < √n.
If we square both sides of the inequality, we get: n is prime saturated if (the largest prime factor of n)² < n
A. 6 = (2)(3) ---> 3² > 6 n is NOT PRIME SATURATED
B. 35 = (5)(7) ---> 7² > 35 n is NOT PRIME SATURATED
C. 46 = (2)(23) ---> 23² > 46 n is NOT PRIME SATURATED
D. 66 = (2)(3)(11) ---> 11² > 66 n is NOT PRIME SATURATED
E. 75 = (3)(5)(5) ---> 5² < 75 n IS PRIME SATURATED
Answer: E
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