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How many positive integers less than 2008 have an even number of divisors?
There are 1,963 such integers. Every factor of a number has a pair. The only time there will be an odd number of factors is if one factor is repeated, ie the number is a perfect square. So the question is really asking: how many positive integers less than 2008 (in the range 1 to 2007) are not perfect squares. √2007 = 44 and a bit (it lies between 44 and 45) So there are 44 integers less than (or equal to) 2007 which are perfect squares → 2007 - 44 = 1963 integers are not perfect squares in the range 1-2007 and have an even number of factors (divisors).
Why is the square root 14 an irrational number?
It can be proven that it is impossible to find a pair of integers, p and q, such that p/q = sqrt(14).
What numbers multiply to 288 and add to 49?
337
Which pair of consecutive whole numbers is the square root of 73 between?
The square root of 73 is between 8 and 9.
What is zero pairs?
A zero pair is when one pairs a positive counter and a negative counter.
What two integers are between the square root of 110?
-3 and 6 is one possible pair.
What is the 2 consecutive integers between which the square root of 30 lies?
THere are two pair of consecutive integers. 52 = 25 < 30 < 36 = 62 So, one pair is 5 and 6 and the other pair is -6 and -5.
What two consecutive integers is the square root off 99 in between?
-10 and -9 is one possible pair.
What is the consecutive number between the square root of 89?
sqrt(89) = -9.4 or +9.4 So one possible pair of consecutive integers between the square roots of 89 are 2 and 3.
What is the lcf of 50 and 35?
The lowest common factor of any pair of positive integers is 1.
Which pair of number does square root 105 fall between?
There is no unique pair of numbers that satisfies these requirements. Suppose a and b is such a pair, and sqrt(105) = x then you want a < x < b But a < (a+x)/2 < x < (b+x)/2 < b So that (a+x)/2 and (b+x)/2 are a closer pair. and you can then find a closer pair still - ad infinitum. The question can be answered (sort of) if it asked about "integers" rather than "numbers". 100 < 105 < 121 Taking square roots, this equation implies that 10 < sqrt(105) < 11 so the answer could be 10 and 11. But (and this is the reason for the "sort of") the above equation also implies that -11 < sqrt(105) < -10 giving -11 and -10 as a pair of consecutive integers. So, an unambiguous answer is possible only if the question specifies positive integers.
What are the rules in adding integers with unlike signs?
For each pair of such integers, find the difference between the absolute values of the two integers and allocate the sign of the bigger number to it.
How many positive integers less than 2008 have an even number of divisors?
There are 1,963 such integers. Every factor of a number has a pair. The only time there will be an odd number of factors is if one factor is repeated, ie the number is a perfect square. So the question is really asking: how many positive integers less than 2008 (in the range 1 to 2007) are not perfect squares. √2007 = 44 and a bit (it lies between 44 and 45) So there are 44 integers less than (or equal to) 2007 which are perfect squares → 2007 - 44 = 1963 integers are not perfect squares in the range 1-2007 and have an even number of factors (divisors).
What number can be multiplied to equal 139?
There are infinitely many numbers, but a simple pair to remember is 1 and 139. Since 139 is a prime, this is the only solution with a pair of positive integers.
What are the two consecutive numbers with the product of 4160?
Assuming you mean consecutive numbers are integers, then: The integers will be the two integers between which the square root of 4160 lies. Calculating the square root of 4160 using the "long" division method: ________6__4 _____---------- ___6|_41_60 _______36 _______--- __124|__560 _________496 _________---- __________64 The square root of 4160 is 64.<something>, thus it lies between 64 and 65, so: 4160 = 64 × 65
A pair of integers whose sum gives an integer smaller than the both integers?
Take any negative integers, say -5 and -10, their sum is -15 which is smaller than both of them. We could have used 0 as well, so I should have said any non-positive integers. To see that is does not work with positive integers, take 5 and 10 whose sum is 15 which is BIGGER than either one.
Every positive rational number and its negative pair?
Every positive rational number and its negative are the two square roots of the same positive rational number.
