# Number Properties II

#### More words of “Wiz-dom” on Order of Operations

The FACTORS of an integer are the integers that divide evenly into it without having a remainder. Every integer (other than 1) has at least two different factors: 1 and itself.

#### More words of “Wiz-dom” on Factors

The MULTIPLES of an integer are the numbers that it divides into evenly. It’s the opposite of factors.

#### More words of “Wiz-dom” on Multiples

A PRIME number is an integer that has exactly two different factors: 1 and itself.

#### More words of “Wiz-dom” on a Prime Number

Integers are PROPORTIONALto one another if they are multiples or factors of one another.

 The test writer wants to know if you understand directly (multiples) and indirectly proportional (reciprocal multiple, e.g., if one quantity is multiplied by 3, the other is multiplied by 1/3).

More words of “Wiz-dom” on Proportional

The REMAINDER is what’s left over if a division problem does not come out evenly.

## Sample Questions

6.  How many prime factors does the number 24 have?

(A) 6
(B) 4
(C) 3
(D) 2
(E) 0

#### 7.  In a division problem x/7, the remainder is r. How many possible odd values for r exist?

(A) 0
(B) 1
(C) 2
(D) 3
(E) 6

18.  If the sum of two consecutive odd numbers is 28, what is their product?

5.  If m/9 is an integer, all of the following are possible values of m EXCEPT?

(A) 18
(B) 81
(C) 171
(D) 271
(E) 297

20.  The sum of x consecutive integers is odd. The first integer in the sequence is even. Which of the following CANNOT be x?

(A) 2
(B) 3
(C) 4
(D) 6
(E) 7