Integer Properties

Question 1

Divisibility rule for 2

Answer 1

All even #s are divisible by 2

Question 2

Disability rule by 5

Answer 2

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

Question 3

Divisibility rule by 3

Answer 3

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

Question 4

Divisibility rule by 9

Answer 4

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

Question 5

Multiple

Answer 5

A number produced by multiplying a smaller number

Question 6

Multiple rules

Answer 6

Every positive integer is a multiple of itself

Question 7

Prime number

Answer 7

A number with only two factors: 1 and itself

Question 8

The prime numbers less than 20 are…

Answer 8

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

Question 9

The prime numbers between 20 and 60 are…

Answer 9

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

Question 10

Counting factors of large numbers

Answer 10

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.

Question 11

First 15 perfect squares

Answer 11

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

Question 12

How to spot a large perfect number when all you’re given are the prime factorization switch exponents?

Answer 12

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.

Question 13

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

Answer 13

Ok

Question 14

Greatest Common Factor/Divisor of any set of numbers is simply…

Answer 14

The biggest common factor, i.e., the biggest of all factors that all the numbers have in common with each number

Question 15

So how to shortcut finding GCF of large sets of numbers

Answer 15

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

Question 16

Shortcut for finding Least Common Multiple/Denominator

Answer 16

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

Question 17

Zero is an even number, but neither positive nor negative

Answer 17

Ok

Question 18

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

Answer 18

Ok

Question 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

Answer 19

Ok

Question 20

Adding and subtracting evens and odds

Answer 20

Add or subtract likes get EVEN

add or subtract unlikes get ODD

Question 21

Multiplying evens and odds

Answer 21

Even with even get EVEN

Odd with odd get ODD

Even with odd get EVEN

Question 22

3 Key terms that will appear on exam

Answer 22

Factor - # that, when multiplied with another #, produces a product

Divisor

Divisible