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There are a total of 5 positive three-digit perfect cubes that are even. To find this, we first determine the range of three-digit perfect cubes, which is from 46 to 96. Then, we identify the even perfect cubes within this range, which are 64, 216, 512, 729, and 1000.
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What is the smallest positive integer that 248832 can be multiplied by in order for the product to be a perfect square?
The prime factorisation of 248832 is 2¹⁰ × 3⁵ Every perfect square number has a prime factorisation where each prime is to an even power. 2 has an even power 3 has an odd power, so need an extra power → multiple 248832 by 3 which gets (2⁵ × 3³)²
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 kind of number is 16?
The number 16 is an integer (a counting or whole number). It is also a positive number, and it is even. Additionally, it is a perfect square, as it is the product of 4 times 4 (which is 4 squared).
What is the sum of the first 100 positive even numbers?
The sum of the first 100 positive even numbers is 10,100.
A negative number raised to an even power will be positive or negative?
Positive
What are the two positive three digit even perfect cubes?
8x8x8 6x6x6
When can a polynomial is said to be sum or difference of two cubes?
When it is of the form x3 + y3 or x3 - y3. x or y can have coefficients that are perfect cubes, or even ratios of perfect cubes eg x3 + (8/27)y3.
Is it true that all polyhedrons are cubes?
No. Not even all hexahedrons are cubes.
What numbers always have an even number of factors?
All positive integers which are not perfect squares.
Is 0 a positive even number?
0 is even, but not positive.
What is the smallest positive integer that 248832 can be multiplied by in order for the product to be a perfect square?
The prime factorisation of 248832 is 2¹⁰ × 3⁵ Every perfect square number has a prime factorisation where each prime is to an even power. 2 has an even power 3 has an odd power, so need an extra power → multiple 248832 by 3 which gets (2⁵ × 3³)²
What is the word for to cut into very small cubes of even sizes?
Cubing.
How many positive factors square numbers have?
Any positive odd number.For example for p = 17 positive factors, consider n^(p-1) for any integer n.Since p is odd, p-1 is even and so n^(p-1) is a perfect square number.
Do odd numbers always have an odd number of factors?
No. Consider 15: 1,3,5,15 Every positive whole number has an even number of factors, unless the number is a perfect square.
Are perfect squares always even?
Yes they are always even, other wise it would not be a perfect sqare.
Can a cube tesselate?
Sure cubes can tessellate. It's actually very easy to do so with cubes, as they would all have straight sides of even lengths from any angle.
What numbers are squares and cubes of other numbers?
All non-negative numbers (including zero) are real-number squares of other numbers.All numbers (positive, negative, and zero) are cubes of other numbers."Numbers" generally refers to the set of all real numbers. 2 is the square of a real number, √2. √2 is not a whole number. It's not even rational. But it is a real number, and therefore meets the criteria specified. Even pi (π), an irrational number itself, is the square of another real number (√π). The only real numbers that cannot be squares are negative numbers, because squares of negative numbers are always positive, because the product of two negative numbers is always positive. This restriction, however, does not apply to cubes, because if you multiply three negative numbers by each other, the result is negative.Now, for the question you may have meant to ask: "What numbers are squares and cubes of whole numbers (integers)?"It would be impossible to list all squares and cubes of integers, because even when you limit it to integers, there is still an infinite number of numbers, and every one of them has both a square and a cube.Examples of integers, their squares, and their cubes.0, 0, 01, 1, 1(-1, 1, -1)2, 4, 8,(-2, 4, -8)3, 9, 274, 16, 645, 25, 12510, 100, 1000Only a very few numbers, such as 0, 1, and 64, are both squares and cubes of integers. Note that 64 is 43 and also 82. (see the related question)
