Integers

Question 1

integer

Answer 1

a number that can be written withut a decimal or fractional component

Question 2

whole numbers

Answer 2

inonnegative integers and 0

Question 3

properties of 0

Answer 3

0x any number=0
0/any numb=0
any numb / 0= undefined (not 0) 
square root of 0 is 0
0^2 =0
0 is the only number that is equal to its opposite (0=-0)
0= multiple of all numbers
0 is even number

Question 4

properties of 1

Answer 4

1^2= 1
1 is odd number
1 is not a prime number

Question 5

even and odd numbers

Answer 5

even= a number must be divisible by 2 without leaving a remainder 
units digit= 0,2,4,6,8
can be represented as= 2n
odd=if it's not divisible by 2 
units digit= 1,3,5,7,9
can be represented as 2n-1 or 2n+1

Question 6

odd+odd=
even+even=
even+odd=
odd-odd=
even-even=
odd-even=
even-odd=

Answer 6

odd+odd=even
even+even=even
even+odd=odd
odd-odd=even
even-even=even
odd-even=odd
even-odd=odd

Question 7

eveneven
evenodd
oddeven
oddodd

Answer 7

eveneven=even
evenodd= even
oddeven= even
oddodd= odd

Question 8

even/odd
odd/odd
even/even

Answer 8

even/odd=even
odd/odd=odd
even/even=even or odd

Question 9

absolute values

Answer 9

is a distance from zero on a number line (hence both -5 and 5 are on the same distance from 0)

Question 10

signed numbers

Answer 10

another way to refer to a positive or negative number

Question 11

+++=

—=

Answer 11

+

-

Question 12

multiplying or dividing two numb with the same sign

Answer 12

the result (product or quotient) is always positive

Question 13

multiplying or dividing two numb with the different sign

Answer 13

the result (product or quotient) is always negative

Question 14

when a nonzero base is raised to an even exponent

Answer 14

the result will always be positive

Question 15

when a nonzero number is raised to an odd exponent

Answer 15

if the original base is positive the result will be positive

if the original base is negative the result will be negative

Question 16

for any positive integers x and y , y is a factor of x if and only

Answer 16

if x/y is an integer

1<= y<=x –> the factors or divisors

Question 17

multiple of a number

x is multiple of y if and only

Answer 17

is the product of that number with any integer
if x/y is an integer
x is a multiple of 5= x/5 is an integer

Question 18

Prime Numbers

Answer 18

any integer greater than 1 that has no factors other than 1 and itself
2 is the only prime number that is even, all the rest are odd

Question 19

first 30 prime numbers

Answer 19

2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97

Question 20

prime factorization

Answer 20

any composite number (a number that is not prime) can be broken down and expressed as the product of its prime factors

Question 21

finding the number of factors of a particular number (including both prime and non-prime factors)

Answer 21

1. find the prime factorization of a number i.e 2,160 = 2^4 * 3^3 * 5^1
2. add 1 to the value of each exponent and then multiply these results =(4+1)(3+1)(1+1)= 40

Question 22

unique prime factors

Answer 22

distinct/different prime factors a number contains

i.e 12= 223 and has 2 distinct prime factors

Question 23

the number of unique prime factors in a number does not change when

Answer 23

that number is raised to a positive integer exponent

Question 24

LCM

Answer 24

smallest positive integer into which all the numbers in set will divide
LCM of 2 and 5= 10

Question 25

how to find LCM

Answer 25

1. prime factorization of each integer
2. of any repeated prime factors take the largest one (3^2 and 3^3 choose the 3^3 one) if we are left with two of the same power (3^2 and 3^2) just take that number once
3. of what is left take all the non repeated prime factors
4. multiply together what you found in the steps 2 and 3
   = the result is the lcm

Question 26

when a set of positive int do not share same p.f. the lcm is calculated by

Answer 26

multiplying those numbers (7,6= 7*6=42)

Question 27

GCF (greatest common factor)

Answer 27

is the largest number that will divide evenly into all of the numbers in the set ( 8,12,16= 4)

Question 28

finding gcf

Answer 28

prime factorization of all numbers and then multiply the left column only up to the number that divides the entire set

Question 29

if the set has no common p.f. the gcf is

Answer 29

1

Question 30

if we know the lcm and gcf of two positive int (x and y) we know the product of x and y

Answer 30

i.e we have two +ve int x and y whose value we dont know, by knowing gcf and lcm we can multiply them together and get the product
xy= LCM(x,y)GCF(xy) or
lcm(x,y)= (X)(Y)/GCF (x,y) and gcf(x,y)=(x)*(y)/lcm(x,y)

Question 31

if we know the lcm of the set we can find all

Answer 31

unique prime factors

Question 32

using lcm to solve repeating pattern questions

Answer 32

i.e. light L flashes every 32 sec and light M flashes every 12 sec. if both lights flash together at 8pm, when will be the next time they’ll flash together?
lcm of 12 and 32= 96 (sec) so it will flash again at 8:01:36pm

Question 33

divisibility

Answer 33

x/y= z +(no remainder) x is dividend (numerator), y is a divisor (denominator) and z is quotient (the result)

Question 34

two positive int x and y, x/y will yield an int if x is a multiple of y or if y is a factor of x

Answer 34

means the result will yield an int 
y is a factor of x 
y is a divisor of x 
y divides into x 
x is multiple of y 
x is dividend of y 
x is divisible by y

Question 35

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

Answer 35

100/20 is an int (=5), the factors of 20 are 1,2,4,5,10,20 -> 100/1, 100/2, 100/4, 100/5, 100/10 will be integers

Question 36

divisibility of exponents with the same base

Answer 36

a^3/a^2= a^3-2= a

Question 37

if x,a,b=int and x is not 0, in order for a^x/a^y to be an int

Answer 37

x>=y

Question 38

if z is divisible by both x and y, then z must be divisible by

Answer 38

the lcm of x and y

Question 39

finding a number of multiples are there between two numbers

i.e. numb of multiples of 4 between 12 and 96 inclusive?

Answer 39

last multiple of x in the range - first multiple in the range / x +1
(96-12/4)+1=22

Question 40

product of 3 consecutive integer is always divisible by

Answer 40

6

Question 41

two consecutive integer will never share the same prime factors
what is their gcf

Answer 41

always 1