Number Properties

Question 1

What is a way to express consecutive even integers?

Answer 1

If n is odd, then (n-1) ( n+ 1) represents 2 consecutive even integers

Question 2

What must the product of n consecutive even integers be divisible by?

Answer 2

( 2 to the n power) times n!

Question 3

If positive integer N divided by positive integer d leaves remainder r, what are the positive values of n?

Answer 3

r, r+ d,r+ 2d,r+ 3d, etc.
N= r, n= r+d, n= r+ 2d, n= r+ 3 d, etc.

Question 4

How can you easily find the value of N when you have 2 remainder statements?

Answer 4

If positive integer N divided by positive integer j leaves w remainder of b, and it N divided by positive integer k leaves a remainder of C, then all possible values of N can be found via the following process:
1. Find the smallest possible value of N
2. Add the LCM of j and K to this smallest value as many times necessary

Question 5

Is zero positive or negative?

Answer 5

Neither

Question 6

What numbers are factors of zero? / zero is multiple of what numbers?

Answer 6

All numbers

Question 7

What is any number raised to the 0 power?

Answer 7

1

Question 8

Is one a prime number?

Answer 8

No, the first prime number is 2

Question 9

How can you represent even numbers?

Answer 9

2n, where n is an integer

Question 10

How can you represent odd numbers?

Answer 10

2n-1 or 2n+1, where n is an integer

Question 11

What are the sums and differences that yield Even numbers?

Answer 11

Odd + odd = even
Even +even = even
Odd - odd = even
Even - even = even

Question 12

What are the sums and differences that yield odd numbers?

Answer 12

Odd + even = odd
Even +odd = odd
Odd - even = odd
Even - odd = odd

Question 13

Is the result of a product of an even number and any integer, odd or even?

Answer 13

Even

Question 14

Is the result of a product of two odd numbers, odd or even?

Answer 14

Odd

Question 15

Is the result of even / odd, odd or even?

Answer 15

Even

Question 16

Is the result of odd / odd, odd or even?

Answer 16

Odd

Question 17

Is the result of even / even, odd or even?

Answer 17

It can be either even or odd

Question 18

If we are given a nonzero number raised to an even exponent, can we determine the sign of the original number?

Answer 18

No

Question 19

If we are given a nonzero number raised to an odd exponent, can we determine the sign of the original number?

Answer 19

Yes

Question 20

Prime numbers less than 100

Answer 20

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 21

How did you find the LCM?

Answer 21

1. Find prime factorization of each integer
2. Of repeated prime factors among the set, take only those with the largest exponents
3. Take all non-repeated prime factors
4. Multiply together what you found in step 2 and 3, the result is the LCM

Question 22

What is the LCM of two integers that share no prime factors?

Answer 22

The LCM is the product of both numbers (xy)

Question 23

What is the greatest common factor?

Answer 23

The largest number that will divide into all numbers in the set

Question 24

How can you find the greatest common factor?

Answer 24

1. Find the prime factorization of each number
2. Identify repeated prime factors
3. Of repeated prime factors, take only those with the smallest exponent
4. Multiply the numbers found in step 3 and thats the GCF
   If no repeated prime factors are found, the GCF is 1

Question 25

If the LCM of x and y is p and the GCF of x and y is q, then xy=pq, that is xy= LCM(x,y) x GCF (x,y)

Question 26

If two or more entities return to a common starting position at various frequencies,then the shortest amount of time it takes for all entities to return total he same starting position will be the LCM

Question 27

Divisibility rules of 3

Answer 27

A number is divisible by 3 if the sum of the digits is divisible by 3

Question 28

Divisibility rules of 4

Answer 28

If the last two digits of a number is divisible by 4, then the number is divisible by 4

Question 29

Divisibility rules of 5

Answer 29

Last digit is either 5 or 0

Question 30

Divisibility rules of 6

Answer 30

If the number is an even number whose digits sum to a multiple of 3

Question 31

Divisibility rules of 8

Answer 31

A number is divisible by 8 if the number is even and the last three digits are divisible by 8

Question 32

Divisibility rules of 9

Answer 32

A number is divisible by 9 if the sum of all the digits is divisible by 9

Question 33

Divisibility rules of 10

Answer 33

Divisible by 10 if the ones digit is zero

Question 34

Divisibility rules of 11

Answer 34

If the sum of the odd-numbered placed digits minus the even-numbered place digits is divisible by 11

Question 35

Divisibility rules of 12

Answer 35

If the number is divisible by both 3 and 4, it is also divisible by 12

Question 36

Pattern for units digits of powers of 3

Answer 36

3-9-7-1

Question 37

Pattern for units digits of powers of 4

Answer 37

4-6

Question 38

Pattern for units digits of powers of 7

Answer 38

7-9-3-1

Question 39

Pattern for units digits of powers of 8

Answer 39

8-4-2-6

Question 40

Pattern for units digits of powers of 9

Answer 40

9-1