By definition, a factor divides the number evenly, leaving no remainder.

The smallest factor of any number is always 1, as 1 divides every integer.

The passage discusses how systemic factors influence wealth distribution, aligning with this statement.

Rearranging the equation to slope-intercept form gives y = (4/5)x - 4, indicating a positive slope.

A periodic function is characterized by repeating values at regular intervals, such as sine and cosine functions.

The inverse of a function is a function only if the original function is one-to-one.

A linear equation in two variables has exactly one solution unless it is a special case (like parallel lines). Here, it is a standard linear equation.

A polynomial function can have at most as many roots as its degree, but not all roots need to be real.

A regular hexagon has all sides and angles equal, making the statement true.

A regular polygon has both equal sides and equal angles, making both statements true.

In an arithmetic progression, the difference between consecutive terms is constant, which is the defining property of an AP.

In an equilateral triangle, all sides are equal and all angles are equal, each measuring 60 degrees.

A number is divisible by 5 if it ends in either 0 or 5.

A number is divisible by 9 if the sum of its digits is divisible by 9.

Factors of a number are the integers that can divide that number without leaving a remainder, while multiples are the result of multiplying that number by an integer. Hence, factors are always less than or equal to multiples.

In a harmonic progression, the terms can indeed be negative, as the definition does not restrict the terms to positive values.

In a harmonic progression, the reciprocals of the terms indeed form an arithmetic progression.

HCF and LCM can be equal when both numbers are the same.

Modular arithmetic is primarily applicable to integers, making the first statement true.

Prime numbers are defined as having exactly two distinct positive divisors: 1 and the number itself.

Compound interest will always be greater than simple interest for the same principal, rate, and time, except for the case of zero interest.

When two lines intersect, the angles opposite each other (vertical angles) are always equal. Therefore, the correct statement is that vertical angles are always equal.

The base-8 number system, also known as octal, uses digits from 0 to 7. Therefore, the correct statement is that it uses digits 0-7.

All quadrilaterals are indeed polygons, as they are defined as shapes with four sides, which fits the definition of a polygon.

The composition of two functions can result in a function or not, depending on the nature of the original functions.

The property of modular arithmetic states that (a + b) mod n = [(a mod n) + (b mod n)] mod n.

The property of exponents states that a^(m+n) = a^m * a^n.

36 is indeed a perfect square as it can be expressed as 6 x 6.

The function f(x) = x^2 is a quadratic function because it can be expressed in the form ax^2 + bx + c.

The graph of a linear equation is always a straight line.