Number Properties Flashcards
what is the only number that is equal to its opposite?
Zero
What is the formula for even numbers?
2K where k is an int
What is the formula for odd numbers?
2k+1 or 2k-1 where k is an int
Multiplication rule for even numbers
even * any number = even
Multiplication rule of odd numbers
odd * odd = odd
Addition rules
even + even = even or odd + odd = even everything else is odd
Subtraction rules
even - even = even or odd - odd = even everything else is odd
X power 2 = 16; what is X?
X can be 4 or -4
X power 3 = -8; what is X?
X = -2
Factors of a prime number X?
itself i.e X and 1
Number of factors of a prime number?
- Prime factorize X 2. then add 1 to exponents and multiply
Rule about unique prime factors of a number
Number of unique prime factors doesn’t change when the number is raised to a positive integer exponent
What are division rules for odd and even numbers?
odd/odd = odd, even/odd = even, even/even = odd or even, odd/even = not possible
What would be the result when multiplying or dividing with numbers having same sign?
greater than zero
X^any even power. what is the sign of X?
can be +ve or -ve
X^any odd power, what is the sign of X?
sign of X^any odd power
What are the prime numbers b/w 1 and 100?
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
What is a multiple?
x is a multiple of y if x/y = r0
What is a factor?
y is a factor of x if x/y = r0
How do you calculate the LCM of X, Y?
- 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.
(x, y). x/y= r0 What is LCM and GCF?
LCM = x; GCF = y
How do you calculate GCF of x, y?
- prime factorize both x and y 2. identify the lowest of repeated pfs 3. multiply what you found in step 2
What is GCF of x, y when x, y don’t share repeated prime factors?
1
What we would know about x, y if we know their LCM and GCF?
product of x and y
x/y; what is divisor and dividend?
y is divisor, x is dividend
when thinking about divisibility, think about what?
prime factorization
z is divisible by x and y, then z must be divisible by what?
LCM of X and Y
What is divisibility rule for 4?
last two digits of a number were divisible by 4
What is divisibility rule for 8?
last three digits of a number were divisible by 8
What is divisibility rule for 6?
divisible by Both 2 and 3
Formula for division?
x/y = q + r/y
How do you convert 4.33 to fraction form?
4 + 33/100
How do you convert 26/6 to decimal form?
4 + 2/6 = 4 + 0.33 = 4.33
Multiplying, subtracting or adding remainders rule
you can add or multiply remainders when you must correct the excess remainders
the range of possible remainders of x/y
0 to y-1
no of trailing zeroes in a number =
number of (2*5) pairs
no of leading zeroes in a number for 1/x if x is an integer and perfect power of 10?
no of digits of x - 2
no of leading zeroes in a number for 1/x if x is an integer and not a perfect power of 10?
no of digits of x -1
number of primes in factorial when the base of divisor is not a prime number?
prime factorize the base divisor and then use the usual strategy
prime factorization of a perfect square contains?
only even exponents
prime factorization of a perfect cube contains?
only exponents that are multiples of 3
How do you identify whether a fraction is terminating decimal or not?
if the divisor of the fraction contains either 2’s or 5s or both, then only its a terminating decimal
When do remainders exhibit patterns?
when +ve ints are divided by a constant divisor or powers of certain base divided by a constant divisor
When do unit digits exhibit patterns?
when a +ve int raised to a power of consecutive ints
when integers with same units are divided by 5, what happens to remainder?
remainder is same
product of n consecutive integers divisible by?
n!
product of n even consecutive integers divisible by?
2^n(n!)
How many numbers b/w 10 and 100 that are both perfect square and perfect cube and what they are?
Only 1; 64
