4 - Properties Of Numbers

Question 1

Which is the only number equal to its opposite?

Answer 1

0 is the only number equal to its opposite: 0 = -0

Question 2

Which numbers are factors of 0

Answer 2

All numbers are factors of 0

Question 3

0 is a multiple of which numbers

Answer 3

0 is a mupltiple of all numbers

Question 4

Which number is the only one equal to all of its multiples

Answer 4

Zero is the only number equal to all of its multiples

Question 5

Zero is not a factor of any number except…

Answer 5

Zero is not a factor of any number except itself (since 0=0*k)

Question 6

Any number raised to the zero power is…

Answer 6

1 (except for 0)

Question 7

Is zero even or odd

Answer 7

Zero is even

Question 8

Which number is a factor of all numbers

Answer 8

1 is a factor of all numbers

Question 9

All numbers are multiples of which number

Answer 9

All numbers aer multiples of 1

Question 10

1 raised to any power = ?

Answer 10

1 raised to any power = 1

Question 11

By which number can you multiply/divide any number without changing them?

Answer 11

Multiplying/dividing any number by 1 doesn’t change number

Question 12

Which is the only number with exactly one factor?

Answer 12

One is the only number with exactly one factor

Question 13

Is 1 a prime number

Answer 13

1 is not a prime number (first prime number is 2)

Question 14

Even/even=

Answer 14

Even, odd or non-integer

Question 15

Even/odd=

Answer 15

Even, non-integer

Question 16

Odd/odd=

Answer 16

Odd or non-integer

Question 17

Odd/even=

Answer 17

Non-integer

Question 18

List the first 25 prime numbers

Answer 18

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 19

Each trailing zero is created by a…

Answer 19

(5 x 2) pair

Question 20

How do you find the number of trailing zeros of a number?

Answer 20

number of (5 x 2) pairs in prime factorization

Question 21

Answer 21

0 (since they have at least one (5 x 2) pair: 5! = 5x4x3x2x1

Question 22

The prime factorization of a perfect square only contains … exponents

Answer 22

Even

Question 23

When is a number divisible by 3

Answer 23

If sum of digits divisible by 3

Question 24

When is a number divisible by 9

Answer 24

If sum of digits is divisible by 9

Question 25

When is a number divisible by 6

Answer 25

If even number AND sum of digits is multiple of 3

Question 26

When is a number divisible by 4

Answer 26

If last two digits are divisible by 4

Question 27

Answer 27

Question 28

What is the unit digits pattern of the powers of 2

Answer 28

2-4-8-6

Question 29

What is the unit digits pattern of the powers of 3

Answer 29

3-9-7-1

Question 30

What is the unit digits pattern of the powers of 4

Answer 30

4-6

Question 31

All powers of 5 end in?

Answer 31

5

Question 32

All powers of 6 end in?

Answer 32

6

Question 33

What is the unit digits pattern of the powers of 7

Answer 33

7-9-3-1

Question 34

What is the units digits pattern of the powers of 8

Answer 34

8-4-2-6

Question 35

What is the units digits pattern of the powers of 9

Answer 35

9-1

Question 36

The units digit pattern of the powers of any integer greater than 9 (e.g. the powers of 12) is the same as

Answer 36

The units digits pattern of the powers of its unit digit

Question 37

If you sum numbers, how do you figure out what the last digit of the sum is going to be without calculating the whole thing

Answer 37

You just sum the last digits of the two numbers (e.g. 12+12 - 2+2 =4, so know that 4 will be last digit)

Question 38

If you multiply two numbers, how do you know what last digit will be without multiplying the whole number

Answer 38

You multiply the last digits of the two numbers (e.g. 12*12, 2*2=4, so know 4 will be last digit)

Question 39

Answer 39

Question 40

Answer 40

Question 41

If x is divisible by 75, it is automatically also divisible by all the … of 75

Answer 41

If x is divisible by 75, it is automatically also divisible by all the *factors* of 75

Question 42

Answer 42

Question 43

If x is divisible by 2 or more numbers (=has those as factors), x must also be divisible by the … of those numbers

Answer 43

LCM

Question 44

Answer 44

Question 45

Is 0 part of the first nine positive integers?

Answer 45

No, 1,2,3,4,5,6,7,8,9 are

Question 46

X is only divisibly by Y, if the prime factorization of X contains the … of Y E.g. 60 divisible by 15

Answer 46

X is only divisibly by Y, if X contains the prime factorization of Y 60 = 2 x 2 x **3** x **5** 15 = **3** x **5**

Question 47

If x is divisibly by y then… (2 points)

Answer 47

1. x is divisible by all the factors of y 2. prime factorization of x contains prime factorization of y

Question 48

Answer 48

Question 49

When adding two numbers, when will result be odd and when even

Answer 49

Different = odd (E+O) Same = even (E+E / O+O)

Question 50

When multiplying two numbers, when will they be even and when odd?

Answer 50

Just one even = even Both odd = odd

Question 51

Will exponents change numbers from being even or odd?

Answer 51

No, they keep being even or odd (E^3=E)