MATH 1350 – Test #3 Review– Comprehensive Study Guide
The Fundamental Theory of Arithmetic - correct answer ✔✔ Each composite
number can be written as a unique product of prime factors.
Even - correct answer ✔✔ A number is even if it has 2 as a factor and it is divisible
by 2. It can be represented by 2q.
Odd - correct answer ✔✔ A number is odd if it does not have a factor or 2, and
when divided by 2, it has a remainder of 1. It can be represented by 2q+1.
Definition of "Divides" - correct answer ✔✔ If a, b are whole numbers, then b
divides a, denoted b | a, if and only if there is a unique whole number q such that
a=bq. (In other words, if a is a multiple of b.)
Divisibility Theorems - correct answer ✔✔ If d | a, then d | na
If d | a and d | b, then d | (a ± b)
If d | a and d ∤ b, then d ∤ (a ± b)
Divisibility Rules - correct answer ✔✔ A whole number is divisible by 2 if and only
if the ones digit is even.
A whole number is divisible by 5 if and only if the ones digit is 0 or 5.
, A whole number is divisible by 10 if and only if the ones digit is 0.
A whole number is divisible by 4 if and only if the two rightmost digits of the
number represent a number that is divisible by 4.
A whole number is divisible by 8 if and only if the three rightmost digits of the
number represent a number that is divisible by 8.
A whole number is divisible by 3 if and only if the sum of its digits is divisible by 3.
A whole number is divisible by 9 if and only if the sum of its digits is divisible by 9.
A whole number is divisible by 6 if and only if it is divisible by both 2 and 3.
Prime number - correct answer ✔✔ A natural number is a prime number if and
only if it has exactly two, distinct, positive divisors. (Why 1 is not a prime number.)
Composite number - correct answer ✔✔ A natural number is a composite number
if and only if it has a positive factor other than one and itself.
Prime factorization - correct answer ✔✔ representing a number as the product of
prime numbers
The Fundamental Theory of Arithmetic - correct answer ✔✔ Each composite
number can be written as a unique product of prime factors.
Even - correct answer ✔✔ A number is even if it has 2 as a factor and it is divisible
by 2. It can be represented by 2q.
Odd - correct answer ✔✔ A number is odd if it does not have a factor or 2, and
when divided by 2, it has a remainder of 1. It can be represented by 2q+1.
Definition of "Divides" - correct answer ✔✔ If a, b are whole numbers, then b
divides a, denoted b | a, if and only if there is a unique whole number q such that
a=bq. (In other words, if a is a multiple of b.)
Divisibility Theorems - correct answer ✔✔ If d | a, then d | na
If d | a and d | b, then d | (a ± b)
If d | a and d ∤ b, then d ∤ (a ± b)
Divisibility Rules - correct answer ✔✔ A whole number is divisible by 2 if and only
if the ones digit is even.
A whole number is divisible by 5 if and only if the ones digit is 0 or 5.
, A whole number is divisible by 10 if and only if the ones digit is 0.
A whole number is divisible by 4 if and only if the two rightmost digits of the
number represent a number that is divisible by 4.
A whole number is divisible by 8 if and only if the three rightmost digits of the
number represent a number that is divisible by 8.
A whole number is divisible by 3 if and only if the sum of its digits is divisible by 3.
A whole number is divisible by 9 if and only if the sum of its digits is divisible by 9.
A whole number is divisible by 6 if and only if it is divisible by both 2 and 3.
Prime number - correct answer ✔✔ A natural number is a prime number if and
only if it has exactly two, distinct, positive divisors. (Why 1 is not a prime number.)
Composite number - correct answer ✔✔ A natural number is a composite number
if and only if it has a positive factor other than one and itself.
Prime factorization - correct answer ✔✔ representing a number as the product of
prime numbers
