2 Unit One VocabularyRectangular 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
3 Divisibility tests 346 715 Χ 450 735 569 Χ 230 455 Χ Divisible by 2A 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 ΧDivisible by 5A number is divisible by 5 if the last digit is 5 or 0450 ΧDivisible by 10A number is divisible by 10 if the last digit is 0230 Χ
4 Divisibility tests continued… Divisible by 3Add up all the digits in the number. If the sum is divisible by 3, so is the whole number. Χ(2+4+6=12) (4+5+1=10)12 is divisible by 3, so is is not divisible by 3, neither is 451Divisible by 4Look 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 ,311 Χ32 is divisible by 4, so is 2, is not divisible by 4, neither is 7,311
5 Divisibility tests continued … Divisible by 6A number is divisible by 6 only if it is both divisible by 2 and 3. ΧDivisible by both 2 & Divisible by 3, but not 2Divisible by 9Add up all the digits in the number. If the sum is divisible by 9, so is the whole number.846 Χ(8+4+6=18) (4+5+1=10)18 is divisible by 9, so is is not divisible by 9, neither is 451
6 Prime numbers – numbers that only have two factors (one and itself.) Composite numbers – numbers that have more than 2 factors
8 Finding all of the factors for a number: Step 1: Always begin with the number one.1 x 24 = 24Step 2: move on to the number two.2 x 12 = 24Step 3: continue on until you start repeatingnumbers.(the next number to check after 4 is doesn’t go into 24 andso you move on to has already been used so you knowyou have found all of your factors.)
11 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) ?
12 Sources:-Everdyay Math Student reference book -Some examples taken from: Mr.Wrinkle.net/unit1