Number Properties

Question 1

what is the only number that is equal to its opposite?

Answer 1

Zero

Question 2

What is the formula for even numbers?

Answer 2

2K where k is an int

Question 3

What is the formula for odd numbers?

Answer 3

2k+1 or 2k-1 where k is an int

Question 4

Multiplication rule for even numbers

Answer 4

even * any number = even

Question 5

Multiplication rule of odd numbers

Answer 5

odd * odd = odd

Question 6

Addition rules

Answer 6

even + even = even or odd + odd = even everything else is odd

Question 7

Subtraction rules

Answer 7

even - even = even or odd - odd = even everything else is odd

Question 8

X power 2 = 16; what is X?

Answer 8

X can be 4 or -4

Question 9

X power 3 = -8; what is X?

Answer 9

X = -2

Question 10

Factors of a prime number X?

Answer 10

itself i.e X and 1

Question 11

Number of factors of a prime number?

Answer 11

1. Prime factorize X 2. then add 1 to exponents and multiply

Question 12

Rule about unique prime factors of a number

Answer 12

Number of unique prime factors doesn’t change when the number is raised to a positive integer exponent

Question 13

What are division rules for odd and even numbers?

Answer 13

odd/odd = odd, even/odd = even, even/even = odd or even, odd/even = not possible

Question 14

What would be the result when multiplying or dividing with numbers having same sign?

Answer 14

greater than zero

Question 15

X^any even power. what is the sign of X?

Answer 15

can be +ve or -ve

Question 16

X^any odd power, what is the sign of X?

Answer 16

sign of X^any odd power

Question 17

What are the prime numbers b/w 1 and 100?

Answer 17

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

Question 18

What is a multiple?

Answer 18

x is a multiple of y if x/y = r0

Question 19

What is a factor?

Answer 19

y is a factor of x if x/y = r0

Question 20

How do you calculate the LCM of X, Y?

Answer 20

1. prime factorize both x and y 2. take the highest of repeated pf 3. identify the non repeated pf 3. multiply what you found in steps two and three.

Question 21

(x, y). x/y= r0 What is LCM and GCF?

Answer 21

LCM = x; GCF = y

Question 22

How do you calculate GCF of x, y?

Answer 22

1. prime factorize both x and y 2. identify the lowest of repeated pfs 3. multiply what you found in step 2

Question 23

What is GCF of x, y when x, y don’t share repeated prime factors?

Answer 23

1

Question 24

What we would know about x, y if we know their LCM and GCF?

Answer 24

product of x and y

Question 25

x/y; what is divisor and dividend?

Answer 25

y is divisor, x is dividend

Question 26

when thinking about divisibility, think about what?

Answer 26

prime factorization

Question 27

z is divisible by x and y, then z must be divisible by what?

Answer 27

LCM of X and Y

Question 28

What is divisibility rule for 4?

Answer 28

last two digits of a number were divisible by 4

Question 29

What is divisibility rule for 8?

Answer 29

last three digits of a number were divisible by 8

Question 30

What is divisibility rule for 6?

Answer 30

divisible by Both 2 and 3

Question 31

Formula for division?

Answer 31

x/y = q + r/y

Question 32

How do you convert 4.33 to fraction form?

Answer 32

4 + 33/100

Question 33

How do you convert 26/6 to decimal form?

Answer 33

4 + 2/6 = 4 + 0.33 = 4.33

Question 34

Multiplying, subtracting or adding remainders rule

Answer 34

you can add or multiply remainders when you must correct the excess remainders

Question 35

the range of possible remainders of x/y

Answer 35

0 to y-1

Question 36

no of trailing zeroes in a number =

Answer 36

number of (2*5) pairs

Question 37

no of leading zeroes in a number for 1/x if x is an integer and perfect power of 10?

Answer 37

no of digits of x - 2

Question 38

no of leading zeroes in a number for 1/x if x is an integer and not a perfect power of 10?

Answer 38

no of digits of x -1

Question 39

number of primes in factorial when the base of divisor is not a prime number?

Answer 39

prime factorize the base divisor and then use the usual strategy

Question 40

prime factorization of a perfect square contains?

Answer 40

only even exponents

Question 41

prime factorization of a perfect cube contains?

Answer 41

only exponents that are multiples of 3

Question 42

How do you identify whether a fraction is terminating decimal or not?

Answer 42

if the divisor of the fraction contains either 2's or 5s or both, then only its a terminating decimal

Question 43

When do remainders exhibit patterns?

Answer 43

when +ve ints are divided by a constant divisor or powers of certain base divided by a constant divisor

Question 44

When do unit digits exhibit patterns?

Answer 44

when a +ve int raised to a power of consecutive ints

Question 45

when integers with same units are divided by 5, what happens to remainder?

Answer 45

remainder is same

Question 46

product of n consecutive integers divisible by?

Answer 46

n!

Question 47

product of n even consecutive integers divisible by?

Answer 47

2^n(n!)

Question 48

How many numbers b/w 10 and 100 that are both perfect square and perfect cube and what they are?

Answer 48

Only 1; 64