Ch. 3 Number Properties Flashcards
What is an integer?
A number that doesn’t have a decimal or fraction:
-100, -20, -1, 0, 3, 13 are all integers
-2.14, Pi, and 1/2 are NOT integers!
Is zero positive or negative?
Neither! There is no sign associated w/ 0
What is a whole number?
Whole numbers are nonnegative integers, so 0 and all positive integers are whole numbers!
What is the only number that is equal to its opposite?
0 = -0
Is zero even or odd?
Even
What is the square root of zero?
0
0^ any positive power = ?
0
0^0 = ?
Undefined, never tested on the GRE
0 * any number = ?
0, so 0 is a multiple of ALL numbers and 0 is equal to all of its multiples
0 is a factor of which numbers?
Only itself, b/c if you multiply anything by 0, it’ll equal 0, so 0 can’t be a factor of 6, for example b/c 0* anything = 0, it can never be 6.
write this algebraically: a is a factor of b
b = a x k, where k is some integer
What number is a factor of ALL numbers?
1
Because k x 1 = k, so 1 is a factor of k
1 ^ any power =
1
if a is any integer, a ^ 0 = ?
1
any number raised to the 0 power is 1 (except 0^0 which is undefined)
ALL numbers are multiples of what number?
1
What numbers have only one factor?
Only 1
All other numbers have at least 1 & itself
Is 1 a prime number?
No, 2 is the first prime number
How can we represent an even integer? An odd integer?
2n for even; 2n +/- 1 for odd
Because all even integers are divisible by 2 w/o a remainder
odd +/- odd =
even
even +/- even
even
even +/- odd
odd +/- even
odd
even x even =
even
even x odd =
even
odd x odd =
odd
If you’re multiplying two or more integers, and any of them are even, the product/ result will be (even/ odd/ can be either one)?
even
What are the results when multiplying evens & odds?
If there are ANY even numbers (no matter how many integers you’re multiplying), then result will be even.
If you’re only multiplying odds, then result is odd.
What are the results when adding/ subtracting evens & odds?
If they’re the same (both even or both odd), then result is even.
If they’re different (even +/- odd), then result is odd.
When an even number is divisible by an even number, is the result even or odd?
It can be either one!
4/2 = 2
6/2 = 3
even / even =
Even OR odd - can be either!
even / odd =
even
odd / odd =
odd
odd / even =
not divisible
What is the absolute value of a number?
The distance between the number & 0 on the number line
When a nonzero base is raised to an even exponent, is the result positive, negative, or either?
Positive, always.
For example,
3^4 = 81
(-2)^2 = 4
(-1/2)^6 = 1/64
When a nonzero base is raised to an odd exponent, is the result positive, negative, or either?
If original base is positive, it’ll be +ve.
If original base is negative, it’ll be -ve.
What does this mean: y is a factor of x?
Y divides evenly into x
2 is a factor of 16
Which number has infinitely many factors?
0
Every number is a factor of 0 b/c every number divides into 0
If a number is positive, what is its smallest factor & largest factor?
1 is smallest, itself is largest, so,
1 <= all factors <= itself
What is another name for factor?
Divisor
2 and 4 are divisors of 16
2 and 4 are factors of 16
For any positive integers x and y, y is a factor of x if and only if what is an integer?
x/y is an integer
Also, 1 <= y <= x
What is a multiple of a number?
A multiple of a number is the product of that number with any integer
Multiple of x = xn
x is a multiple of y only if x = ny where n is an integer
The number x is a multiple of 5, write this algebraically
x = 5n where n is an integer
This means x / 5 is an integer
What is a prime number?
An integer w/ only two factors: one and itself
What are composite numbers?
NOT prime numbers - they have factors OTHER than 1 and themselves