Flashcards in Integer Properties Deck (22)
Divisibility rule for 2
All even #s are divisible by 2
Disability rule by 5
If last digit is 5 or 0, it is divisible by 5
Divisibility rule by 3
If the sum of digits is divisible by 3, then it is divisible by 3
Divisibility rule by 9
Same as 3, but be careful that # has to be divisible by 9, not 3: ie, if # is divisible by 3, but not 9, then it is not divisible by 9
A number produced by multiplying a smaller number
Every positive integer is a multiple of itself
A number with only two factors: 1 and itself
The prime numbers less than 20 are...
2, 3, 5, 7, 11, 13, 17, 19
The prime numbers between 20 and 60 are...
23, 29, 31, 37, 41, 43, 47, 53, 59
Counting factors of large numbers
STEP 1: Break down number into smaller chunks and find the prime factorization, making sure that every exponent is included
STEP 2: Make a list of the exponents of the factors, taking care to see that 1 is also an exponent
STEP 3: Add one to each exponent
STEP 4: Multiply all the numbers together
To add odd factors, do steps 1-4 only on ODD factors.
To add even number factors, subtract grand total of factors with total of odd factors.
First 15 perfect squares
1, 4, 9, 16, 25, 36, 49, 64, 81, 109, 121, 144, 169, 196, 225
How to spot a large perfect number when all you're given are the prime factorization switch exponents?
If all the exponents are even numbers, the unknown multiple must be a perfect square
To figure out the actual factor, reduce all exponents by half, and multiply all factors with newly reduced exponents. Answer is resulting factor squared.
Total factors of a perfect square is always an ODD number since 1 is always added to every exponent of every factor
Greatest Common Factor/Divisor of any set of numbers is simply...
The biggest common factor, i.e., the biggest of all factors that all the numbers have in common with each number
So how to shortcut finding GCF of large sets of numbers
Find all their common prime factors (including their common exponents) and multiply them
Shortcut for finding Least Common Multiple/Denominator
Do a prime factorization of both numbers
Write each number as a factor of their GCF
Multiply the GCF with the other factors
Zero is an even number, but neither positive nor negative
Prime factorization of an even number always includes 2, this can be represented as 2•x or 2x
Odd number is never divisible by 2 and never contain a factor of 0. This can be represeted as 2x + 1, or 2x - 1
Adding and subtracting evens and odds
Add or subtract likes get EVEN
add or subtract unlikes get ODD
Multiplying evens and odds
Even with even get EVEN
Odd with odd get ODD
Even with odd get EVEN