Flashcards in Integer Properties Deck (22)

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1

## Divisibility rule for 2

### All even #s are divisible by 2

2

## Disability rule by 5

###

If last digit is 5 or 0, it is divisible by 5

3

## Divisibility rule by 3

### If the sum of digits is divisible by 3, then it is divisible by 3

4

## 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

5

## Multiple

### A number produced by multiplying a smaller number

6

## Multiple rules

###
Every positive integer is a multiple of itself

7

## Prime number

### A number with only two factors: 1 and itself

8

## The prime numbers less than 20 are...

### 2, 3, 5, 7, 11, 13, 17, 19

9

## The prime numbers between 20 and 60 are...

### 23, 29, 31, 37, 41, 43, 47, 53, 59

10

## 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.

11

## First 15 perfect squares

### 1, 4, 9, 16, 25, 36, 49, 64, 81, 109, 121, 144, 169, 196, 225

12

## 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.

13

## Total factors of a perfect square is always an ODD number since 1 is always added to every exponent of every factor

### Ok

14

## 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

15

## So how to shortcut finding GCF of large sets of numbers

### Find all their common prime factors (including their common exponents) and multiply them

16

## Shortcut for finding Least Common Multiple/Denominator

###
Do a prime factorization of both numbers

Find GCF

Write each number as a factor of their GCF

Multiply the GCF with the other factors

17

## Zero is an even number, but neither positive nor negative

### Ok

18

## Prime factorization of an even number always includes 2, this can be represented as 2•x or 2x

### Ok

19

## Odd number is never divisible by 2 and never contain a factor of 0. This can be represeted as 2x + 1, or 2x - 1

### Ok

20

## Adding and subtracting evens and odds

###
Add or subtract likes get EVEN

add or subtract unlikes get ODD

21

## Multiplying evens and odds

###
Even with even get EVEN

Odd with odd get ODD

Even with odd get EVEN

22