Factors and Multiples

1. Factors and Multiples

2. Division Properties • How do you know if a number is divisible by 2? • The number will end in a 0, 2, 4, 6, or 8 if it is divisible by 2. (Write this down.) Write down which number is divisible by 2 and explain why. 9245618 5464849 9245618 is divisible by 2 because it ends in 8.

3. Division Properties • How do you know if a number is divisible by 3? • The sum of the digits is divisible by 3 if the number is divisible by 3. (Write this down) Is 951456753852 divisible by 3? 9+5+1+4+5+6+7+5+3+8+5+2 = 60 60 is divisible 3 so 951456753852 is divisible 3. If you’re not sure if 60 is divisible by 3 add the digits again. 6+0 = 6, 6 is divisible 3. Is 753214698 divisible by 3? Explain how you know.

4. Division Properties • How do you know if a number is divisible by 4? • If the digit in the tens place is even and the digit in the ones place is a 0, 4 or 8, or if the digit in the tens place is odd and the digit in the ones place is a 2 or 6.(Write this down.) Write down which number is divisible by 4 and explain why. 9245618 5464846 7531512 7531512 is divisible by 4.

5. Division Properties • How do you know if a number is divisible by 5? • The number will end in a 0 or 5. (Write this down.) Write down a 10-digit number that is divisible by 5.

6. Division Properties • How do you know if a number is divisible by 6? • If the number is divisible by 2 and 3 then it is divisible by 6. (Write this down.) Write down which number is divisible by 6 and explain why. 9245618 5464849 1678254 1678254 is divisible by 6.

7. Division Properties • How do you know if a number is divisible by 9? • The sum of the digits is divisible by 9 if the number is divisible by 9. (Write this down) Is 951456753852 divisible by 9? 9+5+1+4+5+6+7+5+3+8+5+2 = 60 60 is not divisible 9 so 951456753852 is not divisible 9. If you’re not sure if 60 is divisible by 9 add the digits again. 6+0 = 6, 6 is not divisible 9. Is 753214698 divisible by 9? Explain how you know.

8. Division Properties • How do you know if a number is divisible by 10? • If the number ends in 0, it is divisible by 10. (Write this down.) Write down a 12 digit number that is divisible by 10.

9. Vocabulary • Prime Number – A number with two distinct factors, 1 and itself. • Composite Number – A number composed of prime numbers. • Factors – Are the numbers you multiply to get another number. • Multiples – Are the result of multiplying a number by an integer.

10. Prime Numbers 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

11. Testing for Primality • Is 29 a prime number? How can we test it? • What are possible factors of 29? 1 and 29 • 2 doesn’t divide evenly into 29, so the number must be greater than 2 and less than 14. • 3 doesn’t divide evenly into 29 so the number must be greater than 3 and less than 9. • 4 doesn’t divide evenly into 29 so the number best be greater than 4 and less than 7. • This leaves us with 5 and 6 which don’t divide evenly. Therefore 29 is a prime number!

12. Factors • What are the factors of 24? 24 1, 24 2, 12 3, 8 4, 6 Find the factors of 36 using this method.

13. Greatest Common Factor What is the greatest common factor of 24 and 36? 24 1, 24 2, 12 3, 8 4, 6 36 1, 36 2, 18 3, 12 4, 9 6, 6

14. Least Common Multiple What is the least common multiple of 24 and 36? 24, 48, 72, 96, 120, 144 36, 72, 108, 144

15. Exit Ticket • Using ALEKS, send me a message with the subject “Factor and Multiples Exit Ticket” • In the body write down the factors for 12 and 15, write down their greatest common factor, and their least common multiple. The quiz for this lesson is available in ALEKS under WHOLE NUMBERS – FACTORS.