Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
#1 RULES FOR DIVISIBILITY IF A Number Is Divisible By: 2 3 4 5 6 8 9 10 The last digit is even (0, 2, 4, 6, 8) The sum of the digits is divisible by 3 The last 2 digits are divisible by 4 (÷2÷2) The last digit is 0 or 5 It is divisible by 2 and 3 The last 3 digits are divisible by 8 (÷2÷2÷2) The sum of the digits is divisible by 9 The last digit is 0 copyright©amberpasillas2010 #2 IS THE NUMBER DIVISIBLE EXACTLY BY? WRITE yes (y) or no (n) REMEMBER: Show the sums for 3, and show the division for 4 and 8. Number 2 3 1) 360 y 3+6 = 9 y 4 30 2) 60 15 2) 30 y 5 y copyright©amberpasillas2010 6 y 8 180 2)360 90 2)180 45 2) 90 y 9 y 10 y #3 FACTOR A Factor is a number that is multiplied by another number to give the product. 7 x 8 = 56 Factors A Factor is the number that divides evenly into another number. 56 ÷ 8 = 7 Factor copyright©amberpasillas2010 #4 Prime & Composite Prime NumbersA Prime number is a whole number with exactly 2 factors, one and itself. Example: 17, 3, 2, 11, 13, 5 Composite NumbersA Composite number is a number that has more than two factors. Example: 9, 30, 64, 8, 40, 69 copyright©amberpasillas2010 #5 Prime Factorization is when you write a number as the product of prime numbers. 36 Circle the prime numbers 2 Factor Tree 18 2 9 3 3 36 2 2 3 3 2 2 36 2 3 copyright©amberpasillas2010 #6 Make A List Making a list can be helpful to keep track of data and to spot any missing data. To make a list start with the lowest possible factor which is 1. Factors of 36 1 x 36 2 x 18 3 x 12 4x9 6x6 We know we didn’t miss any Factors because our list is ORGANIZED! copyright©amberpasillas2010 Factors of 24 1 x 24 2 x 12 3x8 4x6 #7 GCF, Make a List Method #1 GCF is the largest number that is a factor of 2 numbers. It is useful to know this for reducing fractions. Step 1: List all the factors of both numbers. Step 2: Then find the greatest common factor. Ex. Factors of 12 1 x 12 2x 6 3x 4 Factors of 30 1 x 30 2 x 15 3 x 10 5x 6 Common Factors are 1,2,3,6 GCF= 6 This method is only useful if both numbers are small copyright©amberpasillas2010 #8 Find the prime factorization of the 2 numbers. Step 2: Then multiply their common factors. Step 1: 30 12 2 2 15 6 2 3 3 2 23 5 2 3 5 Factors the 2 numbers have in common are: 2 & 3 Multiply the common factors. GCF 2 3 6 copyright©amberpasillas2010 #9 Multiples A number that is added to itself becomes a multiple. Multiples of 3 = 3, 6, 9, 12, 15, 18 . .. Multiples can go on infinitely forever. The least common multiple (LCM) is the least common number that is a multiple of 2 numbers. It is useful to know this for adding fractions. copyright©amberpasillas2010 #10 LCM Make a List Method # 1 TO FIND THE LCM OF 4 and 12: 1) List the multiples of both numbers 4 = 4, 8, 12, 16, 20… 12 = 12, 24, 36… 2) Find the least multiple that both numbers have in common. LCM is 12 This method is useful if both numbers are small. copyright©amberpasillas2010 #11 LCM Prime Factorization Method # 2 1) List the prime factorization to find the LCM. 20 18 2 2 10 9 3 3 2 2 3 3 2) 3) 5 2 25 Select all common factors once. Select all remaining factors, and multiply. LCM 180 LCM 2 332 5 copyright©amberpasillas2010