Rules of Divisibility

Chapter 7

Rule of “2”

 If the number ends with:0, 2, 4, 6, or 8  It is divisible by 2  Divisible=Divide  Divisible means a number can go into another number evenly with no remainder

The Rule of “2”

 Example:  48, 56, 22, 10 and 34  Are all divisible by 2  Explain why: They all end with a number that is divisible by 2

Practice

 88, 95, 108, 2004, 26, 44  Which number is

not

divisible by “2”  Answer 95  Explain why?

 5 is not divisible by 2

Rule of “5”

 Rule of “5”  The number must end with 5 or 0  Example: 550  Ends with 0, so it is divisible by 5

Practice

 Which numbers are divisible by 5 ?

 262, 265, 360, 455 and 291  Answer:  265  360  455  Explain why?

 The numbers end 5 or 0

Rule of “10”

 Rule of 10  The number has to end with 0 to be divisible by 10  Example: 690  Ends with 0, so 690 is divisible by 10

Practice

 Which number is divisible by 10  550 or 600  Answer  Both 550 and 600  Explain why: They both end with 0

Rule of “4”

 Rule of “4”  The last two digits of a number must be divisible by 4  Example: 444  Take the last two digits of the number 444  Divide by 4: 44 ÷4= 11  444 is divisible by 4

Practice

 Which number is divisible by 4  460 or 328  Answer  Both  Why?  4 can go into 28 evenly  4 can go in 60 evenly

Rule of “3”

 The sum of the digits must be divisible by 3  Example: 240  Add up each digit: 2 + 4 + 0 = 6  Now divide 6 ÷3=2  3 goes into 6 with no remainder so 240 is divisible by 3

Practice

 Which number is divisivble by 3  24 or 81  Answer  Both  Why?

 2 + 4=6, three goes into six evenly  8 + 1= 9 three goes into nine evenly

Rule of 9

 The sum of the digits must be divisible by 9  Example: 360  3 + 6 + 0 = 9  Now take the sum which is “9” and divide  9 ÷ 9 = 1  360 is divisible by 9

Practice

 Which number is divisible by 9?

 540 or 361  Answer  540  Why 5 + 4 + 0 = 9  9 goes into 9 evenly with no remainder