Number Theory GONE WILD! Fun and Games Number Theory GONE WILD! Factors “Fall” into Families Multiples Multiply like Rabbits!

What am I Learning Today? Divisibility Rules How will I show that I learned it? Create a graphic organizer that contains the divisibility rule, an example and an explanation. Use divisibility rules to determine the characteristics of numbers.

Then, try to identify “What’s the rule?” Turn to a partner and try to figure out what the “yes” numbers have in common YES NO 2 43 64 11 128 313 16 25 YES NO 10 24 65 33 225 79 610 246 Then, try to identify “What’s the rule?”

48 is divisible by both 2 and 3 Divisibility Rules A number is divisible by. . . Example Explanation 2 if the last digit is even (0, 2, 4, 6, or 8). 3,978 8 is even 3 if the sum of the digits is divisible by 3. 315 3 + 1 + 5 = 9 9 is divisible by 3 4 if the last two digits form a number divisible by 4. 8,512 12 is divisible by 4 5 if the last digit is 0 or 5. 14,975 The last digit is 5 6 if the number is divisible by both 2 and 3 48 48 is divisible by both 2 and 3 9 if the sum of the digits is divisible by 9. 711 7 + 1 + 1 = 9 9 is divisible by 9 10 if the last digit is 0. 15,990 The last digit is 0

Checking Divisibility Tell whether 462 is divisible by 2, 3, 4, and 5. 2 3 4 5 The last digit, 2, is even. Divisible The sum of the digits is 4 + 6 + 2 = 12. 12 is divisible by 3. Divisible The last two digits form the number 62. 62 is not divisible by 4. Not divisible Not divisible The last digit is 2. So 462 is divisible by 2 and 3.

Checking Divisibility Tell whether 540 is divisible by 6, 9, and 10. 6 9 10 The number is divisible by both 2 and 3. Divisible The sum of the digits is 5 + 4 + 0 = 9. 9 is divisible by 9. Divisible The last digit is 0. Divisible So 540 is divisible by 6, 9, and 10.

Turn to a partner and discuss the following: Paired Discussion Turn to a partner and discuss the following: How can the divisibility rules help you identify composite numbers? If a number is divisible by 4 and 9, by what other numbers is it divisible? Explain.