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UNIT ONE VOCABULARY

Rectangular array: an arrangement of objects in rows and columns. Each row has the same number of objects and each column has the same number of objects.

Factors – numbers that you multiply together to get a product

Factor pair – two numbers that you multiply together to get a product.

Product – the answer you get when you multiply factors together

Divisibility - A number is divisible by another number if it goes in evenly (no remainder)

Composite number – a number that has more than 2 factors

Prime number – a number that has exactly 2 factors (1 and itself)

Square number – a number that makes a square array (2x2, 4x4, 5x5, etc.)

Exponential notation - numbers written with exponents

Exponent - a small number written to the right and above the base number to show how many times the base number is multiplied by itself.

Square root – when you “unsquare” a square number. (example: The square root of 36 is 6 (6x6 =36))

Prime factorization - writing a number as a product of all prime numbers

DIVISIBILITY TESTS

Divisible by 2

A number is divisible by 2 if the last digit (number in the one’s place ) is even or 0

(2, 4, 6, 8, 0)

346 715 Χ

Divisible by 5

A number is divisible by 5 if the last digit is 5 or 0

450 735 569 Χ

Divisible by 10

A number is divisible by 10 if the last digit is 0

230 455 Χ

DIVISIBILITY TESTS CONTINUED…

Divisible by 3

Add up all the digits in the number. If the sum is divisible by 3, so is the whole number.

246 451 Χ (2+4+6=12) (4+5+1=10)

12 is divisible by 3, so is 246 10 is not divisible by 3, neither is 451

Divisible by 4

Look at the last two digits of a number. If the number that the two digits form is divisible by 4, so is the whole number.

2,232 7,311 Χ32 is divisible by 4, so is 2,232 11 is not divisible by 4, neither is

7,311

DIVISIBILITY TESTS CONTINUED …

Divisible by 6

A number is divisible by 6 only if it is both divisible by 2 and 3.

342 741 ΧDivisible by both 2 &3 Divisible by 3, but not 2

Divisible by 9

Add up all the digits in the number. If the sum is divisible by 9, so is the whole number.

846 451 Χ (8+4+6=18) (4+5+1=10)

18 is divisible by 9, so is 846 10 is not divisible by 9, neither is 451

Prime numbers – numbers that only have two factors (one and itself.)

Composite numbers – numbers that have more than 2 factors

Finding all of the factors for a number:

Step 1: Always begin with the number one. 1 x 24 = 24 Step 2: move on to the number two. 2 x 12 = 24

Step 3: continue on until you start repeating numbers. (the next number to check after 4 is 5. 5 doesn’t go into 24 and so you move on to 6. 6 has already been used so you know you have found all of your factors.)

PRIME FACTORIZATION: WRITING A NUMBER AS A PRODUCT OF ALL PRIME FACTORS

Step 1: Divide number into a any factor pair.

Step 2: Circle any number that can't be broken

down any more (prime).

Step 3: Continue to break down numbers until

you are left with all prime numbers.

Step 4: Connect all prime numbers with

x symbols from least to greatest. 3 x 3 x 5

If possible, write your answer in exponential notation 3² x 5

Check: What is 3 x 3 x 5 (or 3² x 5) ?

SOURCES:

-Everdyay Math Student reference book

-Some examples taken from: Mr.Wrinkle.net/unit1