Prime Factorization (Factor Trees) Greatest Common Factor Prime Numbers Composite Numbers Factors Prime Factorization (Factor Trees) Multiples Least Common Multiple Greatest Common Factor Divisibility Rules

Divisibilty Rules Number It is divisible if… 2 A number ends in Examples Examples that to support do not work. 2 A number ends in 0, 2, 4, 6, 8 10, 12, 14 15, 17, 79 36, 98 3 The sum of the digits is divisible by 3 3, 6, 12, 135 142, 17, 23 4 If the last two digits are divisible by 4 or the number ends in 00. 44, 100, 124 41, 77, 38 120, 112 114, 14 5 If the number ends in 5 or 0. 10, 25, 55, 135 41, 77, 88 6 If the number is divisible by 2 and 3. 6, 12, 24, 19, 44, 50 9 If the sum of the digits is divisible by 9. 9, 18, 189, 981 38, 980, 98 10 If the number ends in 0. 10, 20, 30, 1090 125, 38, 88 Divisibilty Rules

Prime Numbers A PRIME number is a number that has only two factors: 1 and itself. Example: 2: only 1 and 2 will go into 2 3: only 1 and 3 will go into 3 5: only 1 and 5 will go into 5 Other prime numbers are : 7, 11, 13, 17, 19, 23, and many more!

Greatest common Factor (GCF) To find the GCF do the following: Step 1: List all the factors for each number Step 2: Find the largest factor these two numbers have in common Example: Find the GCF for 60 and 72 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 The largest number 60 and 72 have in common is 12, therefore the GCF = 12

Least Common Multiple To find the least common multiple do the following: Step 1: List the multiples for each number Step 2: Find the smallest number they have in common other than zero. Example: Find the LCM for 7 and 5 7: 0, 7, 14, 21, 28, 35, 42, … 5: 0, 5, 10, 15, 20, 25, 30, 35, 40, 45, …

Quiz: Factors List the factors each number. Then check your answer by clicking the “CHECK” button. List the factors of 8: List the factors of 10: List the factors of 4: List the factors of 20: List the factors of 16: List the factors of 25: List the factors of 100: List the factors of 3: REVIEW CHECK

Answers: Factor Quiz List the factors each number. Then check your answer by clicking the “CHECK” button. List the factors of 8: 1, 2, 4, 8 List the factors of 10: 1, 2, 5, 10 List the factors of 4: 1, 2, 4 List the factors of 20: 1, 2, 4, 5, 10, 20 List the factors of 16: 1, 2, 4, 8, 16 List the factors of 25: 1, 5, 25 List the factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100 List the factors of 3: 1, 3 REVIEW Back to Quiz

Composite Numbers Composite numbers are numbers that have more than two factors. Example: 4: 1, 2 and 4 go into 4 6: 1, 2 , 3 and 6 go into 6 8: 1, 2, 4, and 8 go into 8.

QUIZ Factors Factors are numbers that go into another number. To find the factors of a number, find the pairs. Example: Factors of 20 1 x 20 2 x 10 4 x 5 20: 1, 2, 4, 5, 10, 20 Then write them in order from least to greatest! Then write them in order from least to greatest! Factors of 50: 1 x 50 2 x 25 5 x 5 50: 1, 2, 5, 25, 50 Remember: A factor will never be larger than the number itself.

Prime Factorization (Factor Trees) QUIZ Prime Factorization (Factor Trees) Factor Trees are used to find the PRIME FACTORIZATION of a number. 70 35 2 5 7 Circle the number if it is prime Prime Factorization of 70 is: 2 x 5 x 7

Multiples are infinite, QUIZ Multiples Multiples are all the numbers a number will go into. Multiples are infinite! Examples: Multiples of : 5: 0, 5, 10, 15, 20, … 3: 0, 3, 6, 9, 12, 15, 18, … 20: 0, 20, 40, 60, … 0 is the first multiple of every number. Multiples are infinite, so you must end each line with … to show infinity.

Quiz: Prime Factorization List the prime factorization for each number. Then check your answer by clicking the “CHECK” button. 72 50 100 90 20 15 CHECK REVIEW

Answers: Prime Factorization Quiz 72: 2 x 3 50: 5 x 2 100: 5 x 2 90: 3 x 5 x 2 20: 2 x 5 15: 3 x 5 3 2 2 2 2 2 2 Back To The Quiz REVIEW

Quiz: Multiples List the multiples for each number. Then check your answer by clicking the “CHECK” button. List the multiples of 8: List the multiples of 10: List the multiples of 4: List the multiples of 20: List the multiples of 16: List the multiples of 25: List the multiples of 100: List the multiples of 3: CHECK REVIEW

Answers: Multiple Quiz List the multiples of 8: 0, 8, 16, 24, 32, … List the multiples of 10: 0, 10, 20, 30, 40,… List the multiples of 4: 0, 4, 8, 12, 16, … List the multiples of 20: 0, 20, 40, 60, 80, … List the multiples of 16: 0, 16, 32, 48, 64, … List the multiples of 25: 0, 25, 50, 75, 100, … List the multiples of 100: 0, 100, 200, 300, 400, … List the multiples of 3: 0, 3, 6, 9, 12, … BACK TO THE QUIZ REVIEW