Number Properties Flashcards
What is a way to express consecutive even integers?
If n is odd, then (n-1) ( n+ 1) represents 2 consecutive even integers
What must the product of n consecutive even integers be divisible by?
( 2 to the n power) times n!
If positive integer N divided by positive integer d leaves remainder r, what are the positive values of n?
r, r+ d,r+ 2d,r+ 3d, etc.
N= r, n= r+d, n= r+ 2d, n= r+ 3 d, etc.
How can you easily find the value of N when you have 2 remainder statements?
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
Is zero positive or negative?
Neither
What numbers are factors of zero? / zero is multiple of what numbers?
All numbers
What is any number raised to the 0 power?
1
Is one a prime number?
No, the first prime number is 2
How can you represent even numbers?
2n, where n is an integer
How can you represent odd numbers?
2n-1 or 2n+1, where n is an integer
What are the sums and differences that yield Even numbers?
Odd + odd = even
Even +even = even
Odd - odd = even
Even - even = even
What are the sums and differences that yield odd numbers?
Odd + even = odd
Even +odd = odd
Odd - even = odd
Even - odd = odd
Is the result of a product of an even number and any integer, odd or even?
Even
Is the result of a product of two odd numbers, odd or even?
Odd
Is the result of even / odd, odd or even?
Even
Is the result of odd / odd, odd or even?
Odd
Is the result of even / even, odd or even?
It can be either even or odd
If we are given a nonzero number raised to an even exponent, can we determine the sign of the original number?
No
If we are given a nonzero number raised to an odd exponent, can we determine the sign of the original number?
Yes
Prime numbers less than 100
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
How did you find the LCM?
- Find prime factorization of each integer
- Of repeated prime factors among the set, take only those with the largest exponents
- Take all non-repeated prime factors
- Multiply together what you found in step 2 and 3, the result is the LCM
What is the LCM of two integers that share no prime factors?
The LCM is the product of both numbers (xy)
What is the greatest common factor?
The largest number that will divide into all numbers in the set
How can you find the greatest common factor?
- Find the prime factorization of each number
- Identify repeated prime factors
- Of repeated prime factors, take only those with the smallest exponent
- Multiply the numbers found in step 3 and thats the GCF
If no repeated prime factors are found, the GCF is 1
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)
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
Divisibility rules of 3
A number is divisible by 3 if the sum of the digits is divisible by 3
Divisibility rules of 4
If the last two digits of a number is divisible by 4, then the number is divisible by 4
Divisibility rules of 5
Last digit is either 5 or 0
Divisibility rules of 6
If the number is an even number whose digits sum to a multiple of 3
Divisibility rules of 8
A number is divisible by 8 if the number is even and the last three digits are divisible by 8
Divisibility rules of 9
A number is divisible by 9 if the sum of all the digits is divisible by 9
Divisibility rules of 10
Divisible by 10 if the ones digit is zero
Divisibility rules of 11
If the sum of the odd-numbered placed digits minus the even-numbered place digits is divisible by 11
Divisibility rules of 12
If the number is divisible by both 3 and 4, it is also divisible by 12
Pattern for units digits of powers of 3
3-9-7-1
Pattern for units digits of powers of 4
4-6
Pattern for units digits of powers of 7
7-9-3-1
Pattern for units digits of powers of 8
8-4-2-6
Pattern for units digits of powers of 9
9-1
