Quant Ch 3 - Properties of Numbers

Question 1

Integer

Answer 1

A number with out a decimal or fractional component

Question 2

x⁰

Answer 2

= 1 when x ≠ 0

Question 3

The first prime number

Answer 3

2. 1 is not prime

Question 4

Representation of even integers

Answer 4

2n

Question 5

Representation of odd integers

Answer 5

2n-1 or 2n+1

Question 6

Addition rules for even and odd numbers

Answer 6

O+O = E
E+E = E
O+E = O
E+O = O

Question 7

Subtraction rules for even and odd numbers

Answer 7

O-O = E
E-E = E
O-E = O
E-O =O

Question 8

Multiplication rules for even and odd numbers

Answer 8

ExE = E
ExO = E
OxO = O

Question 9

Division rules for even and odd numbers

Answer 9

E/O = E
O/O = O
E/E = O or E

Only apply when 1 integer divides evenly into another integer

Question 10

Factors

Answer 10

Numbers that divide into a larger number evenly

Question 11

Multiples

Answer 11

The product of a number with any integer

Question 12

Prime numbers

Answer 12

Numbers that have no other factors other than 1 and itself

Question 13

Composite number

Answer 13

Any number that is not a prime number

Question 14

Prime factorization

Answer 14

When a composite number is broken down and expressed as the product of its prime factors

Question 15

Finding the number of factors of an integer

Answer 15

1) find the prime factorization of the number
2) Add 1 to the value of each exponent & multiply the results

Question 16

Unique prime factors

Answer 16

The number of prime factors that are different in a prime factorization. The number of unique prime factors in a number does not change when the number is raised to a positive integer exponent

Question 17

Least common multiple (LCM)

Answer 17

Smallest positive integer into which all of the numbers in a set will divide

Question 18

Finding the LCM

Answer 18

1) find the prime factorization
2) of any repeated prime factors, take the highest exponent once
3) take all non-repeated prime factors of the integers
4) multiply what’s found in steps 2-3. the result is the LCM

In any set of (+) integers, the LCM is ≥ the largest number in the set

Question 19

Repeated prime factors

Answer 19

A prime factor is repeated when that prime factor is shared by at least 2 of the numbers in a set

Question 20

Integers with no common prime factors

Answer 20

If a set of positive integers share no prime factors, the LCM is the product of the set of numbers

Question 21

Greatest common factor (GCF)

Answer 21

Largest number that will divide into all numbers in a set

Question 22

Find the GCF

Answer 22

1) find the prime factorization
2) of any repeated prime factors, use the factors with the smallest exponent
3) multiply the factors in step 2

If there are no prime factors in common, the GCF is 1

In any set of (+) integers, the GCF is ≤ the smallest number in a set

Question 23

LCM and GCF when 1 integer divides into another evenly

Answer 23

Given 2 positive integers x and y, if it is known that y divides into x evenly then:

LCM (x,y) = x
GCF (x,y) = y

xy = LCM(x,y) x GCF(x,y)

Question 24

How to use the LCM to find unique prime factors

Answer 24

If we know the LCM of a set of (+) integers, the prime factors of the LCM = the unique prime factors of the whole set

Question 25

How to use the LCM for repeated pattern questions

Answer 25

When trying to determine when 2 processes that occur at differing rates or times will coincide, the answer is the LCM *unique question

Question 26

Even division

Answer 26

When the numerator of a (+) fraction is a multiple of the denominator (and vice versa)

Question 27

How to approach divisibility questions

Answer 27

Easiest way to determine whether x is a multiple of y is to prime factorize x and y

Question 28

Factors of factors rule

Answer 28

In x/y, if x is divisible by y, then x is also divisible by all factors of y

Question 29

Divisibility with exponents

Answer 29

x^a / x^b = x^a-b

Question 30

Formula for division

Answer 30

x/y = Q + r/y x = Qy +r Q = x-r/y r = x-Qy

Question 31

Multiplying remainders rule

Answer 31

When determining the remainder of x and x is the product of positive integers, the remainder of x is the product of the remainders of each positive integer *do a practice problem on this if it doesn't make sense

Question 32

Determining the number of trailing zeros of a number

Answer 32

If the prime factorization of a number contains a (5x2) pair, that pair corresponds to 1 trailing zero in the number Any factorial ≥ 5 will always have zero as its units digit

Question 33

Leading zeros in decimals

Answer 33

0.2 = no leading zeros 0.02 = 1 leading zero

Question 34

Determining the number of leading zeros in a decimal

Answer 34

If x is an integer with k digits, and if x is not a perfect power of 10, then 1/x will have k-1 leading zeros

Question 35

Perfect squares

Answer 35

When the square root of an integer x is and integer, x is a perfect square

Question 36

All perfect squares end in...

Answer 36

0,1,4,5,6, or 9

Question 37

The prime factorization of a perfect square will contain only

Answer 37

even exponents

Question 38

Perfect cube

Answer 38

A number (not 0 or 1) that all prime factors have exponents that are divisible by 3

Question 39

Terminating decimals

Answer 39

Decimals that have a finite number of digits

Question 40

Determining whether a decimal is terminating

Answer 40

Any fraction with a denominator whose prime factorization contains ONLY 2s or 5s or both, produces decimals that terminate

Question 41

Remainders after division by 10

Answer 41

When an integer is divided by 10, the remainder will be the units digit of the numerator

Question 42

Remainders after division by 5

Answer 42

When integers in a set with the same units digit are divided by 5, the remainder is constant between them