Study Guide: “Characteristics of Certain Rational Numbers”
 Odd/Even
 Prime/Composite
TEST DATE: ___________
Vocabulary:
1. Product: The number that is the result of multiplying two or more factors (the answer in
a multiplication problem).
product
factor
factor
Ex. 2 x 6 = 12
2. Factors: Numbers that are multiplied to get a product. Factors are the “ingredients,”
the smaller numbers that when multiplied together create a larger number.
Ex. Factors of 12: 1, 2, 3, 4, 6, 12
or factors can be written as multiplication expressions:
12: 1 x 12, 2 x 6, 3 x 4
3. Multiple: The product of a whole number and any other whole number. Multiples are
“multiplied.”
Ex. Multiples of 2: 2 (2 x 1), 4 (2 x 2), 6 (2 x 3)…
4. Prime number: A whole number greater than 1 that has exactly two factors, itself and 1.
0 & 1 are neither prime nor composite. 2 is the only even prime number.
5. Composite number: A whole number greater than one that has more than two factors.
6. * Prime factorization: Writing a number as a product of only its prime factors.
Ex. Prime factors of 12: 2 x 2 x 3
Q: How is this different from “all factors of 12: 1, 2, 3, 4, 6, 12” ?
A: All factors of 12 includes some factors which are composite numbers.
7. Factor pair: A pair of numbers whose product equals a given number.
Ex. “2 x 6” is a factor pair of 12
8. Divisible: A number is divisible by another number if there is no remainder after dividing.
Divisibility Rules: These rules make finding factors of numbers with many digits easier. A
number is divisible (“can be divided by with no remainder”)……
2
3
4
5
6
9
10
if the number is even.
if the sum of the digits of the number is
divisible by 3.
if the last 2 digits are divisible by 4.
if the last digit of the number is 0 or 5.
if the number is divisible by both 2 and 3.
if the sum of the digits is divisible by 9.
If the last digit in 0.
Evens/Odds:
 Explain in words and demonstrate with illustrations that a given number is even or odd.
See “Partners & Leftovers” in class work section of INB.
 From “Partners & Leftovers” (INB) explain the results of:
1. Adding two even numbers (the sum is always even)
2. Adding two odd numbers (the sum is always ____________)
3. Adding one odd and one even number (the sum is always __________)
4. Multiplying two even numbers (the product is always ___________)
5. Multiplying two odd numbers (the product is always __________)
6. Multiplying one odd and one even number (the product is always ____)
Practice Problems: TB pp. 162 – 166, p.
194 Set 3-10 and Set 3-11, p. 198 Set 310 and Set 3-11.