Integer Properties Flashcards
Integers
negatives, 0, positives, no fractions
Factor is the
Lower number
1 is a factor
Of every integer
Factor
Divisor
Factors include
Both positive and negative factors
Divisible by 4
If the last two digits are divisible by 4 then the number is divisible by 4
Divisible by 6
Divisible by 2 and 3
Divisible by 9
Sum of digits divisible by 9
Divisible by 12
Divisible by 4 and 3
Number * (0,1,2,3,4)
Multiples
Every positive integer
Is a multiple of 1
*If we know 7 is a factor of 2401 then a new multiple of 7 could be
2401 + 7; 2401 - 7
*If P and Q are multiple of 7
Then P+Q, P-Q, P *Q are multiples of 7 (700 and 14)
*If k is a multiple then
nk is a multiple
Prime numbers under 60
2,3,5,7,11.13,17,19,23,29,31,37,41,43,47,53,59
Only even prime number
2
To test if a number less than 100 is prime
Check if its divisible by 2,3,5, or 7
Find odd factors
Use the prime factorization methods but just avoid the factors of 2
Find even factors
Total factors- odd factors
Exponents of the prime factors of a perfect square must be
Even because the number of factors double up; so if all the factors are even then its a perfect square; half of those factors give you the square root
The number of factors that the perfect square has
odd because you add one to all the even factors and then multiply
The only integers that have an odd number of factors are
Perfect squares
GCF
1) Find prime factorizations
2) Take common factors
LCM
1) Find prime
2) Take common and then multiple with the remaining
3) My way
LCM of two numbers
Multiple the two numbers/ gcf
Is 0 even
Yes
Do even and odd include positive and negative?
Yes
Odd numbers can be expressed as
2k+ or - 1
Adding/subtracting
Similar even e,e; o,o
Different odd e,o
Multiplying
Multiply anything with even is even, o*o=o
If they don’t tell us that they are integers***
They can be fractions!
Testing cases
Plug in numbers in fours cases: e,o;e,e;o,o;o,e
A set of n consecutive integers
At least one number divisible by n
For consecutive integer, if n is odd then
The sum of a set of consecutive integers is divisible by n
If there are 4 (even) consecutive integers then
2 even and 2 odd; divide total by half
If we have odd number of integers consecutive
There is atleast one divisible by 3
Difference between low and high
Does not matter where it is on the number line
51-511
Dividend/Divisor=
Quotient+ remainder/divisor and this last part is the decimal
Dont forget about 0’s and negatives
n
