5 Minute Check Determine the missing digit to make the statement true. Complete on the back of your homework. 1. 1,376, ?59 is divisible by 3. 2. 1,376,

Tuesday, Oct 30

5 Minute CheckDetermine the missing digit to make the statement true. Complete on the back of your homework.1. 1,376, ?59 is divisible by 3. 2. 1,376, 1?0 is divisible by 2.3. 1,376, ?59 is divisible by 5.4. 1,376, 15? is divisible by 10.5 Minute CheckDetermine the missing digit to make the statement true. Complete on the back of your homework.1. 1,376, ?59 is divisible by 3. 5 Minute CheckDetermine the missing digit to make the statement true. Complete on the back of your homework.1,376, ?59 is divisible by 3.

1 + 3 + 7 + 6 + 5 + 9 = 31

3 + 1 = 4, so the missing digit can be either 2, 5 or 8.5 Minute CheckDetermine the missing digit to make the statement true. Complete on the back of your homework.2. 1,376, 1?0 is divisible by 2.5 Minute CheckDetermine the missing digit to make the statement true. Complete on the back of your homework.1,376, 1?0 is divisible by 2.

Since the last digits is zero, the missing digit can be any digit. 5 Minute CheckDetermine the missing digit to make the statement true. Complete on the back of your homework.3. 1,376, ?59 is divisible by 5.5 Minute CheckDetermine the missing digit to make the statement true. Complete on the back of your homework.1,376, ?59 is divisible by 5.

Since the last digit must be a 0 or 5 to be divisible by 5, and the last digit is 9, this number can never be divisible by 5. 5 Minute CheckDetermine the missing digit to make the statement true. Complete on the back of your homework.4. 1,376, 15? is divisible by 10.5 Minute CheckDetermine the missing digit to make the statement true. Complete on the back of your homework.4. 1,376, 15? is divisible by 10.

The missing digit must be 0. Tuesday, Aug 25Review Lesson 4

Divisibility Patterns

Divisibility PatternsObjective: To understand divisibility patterns.

Divisibility PatternsDivisibility patterns or rules enable one to determine if two whole numbers are evenly divisible. Divisibility PatternsIs 4578 divisible by 4?

Divisibility PatternsIs 4578 divisible by 4?

Divisibility Rule of 4: If the last two digits are divisible by 4, the entire number is divisible by 4.



78 is not divisible by 4, since 4 x 20 = 80 and 78 is 2 less than 80.



Are all numbers divisible by 4 divisible by 2?



Are all numbers divisible by 4 divisible by 2?Yes, since any number divisible by 4 will be even.



Can an odd number by divisible by 4?



Can an odd number by divisible by 4?No, an odd number can never by divisible by an even number.



Divisibility Rule of 6: If the Divisibility Rule of 2 AND 3 works, the entire number is divisible by 6.


Divisibility Rule of 6: If the Divisibility Rule of 2 AND 3 works, the entire number is divisible by 6. The number is even so it is divisible by 2 and the sum of the digits is 6, which is divisible by 3. Since both rules work, the number is divisible by 6.


Divisibility Rule of 6: If the Divisibility Rule of 2 AND 3 works, the entire number is divisible by 6.

Why rules for 2 and 3? Why not 3 and 4? Or 2 and 5?



Divisibility Rule of 9: If the sum of the digits is 9, then the original number is divisible by 9. If the sum is more than one digit, add again.


Divisibility Rule of 9: If the sum of the digits is 9, then the original number is divisible by 9. If the sum is more than one digit, add again.

4 + 5 + 7 + 8 = 24, 2 + 4 = 6 9.

Divisibility Patterns819Is this number divisible by 2,3,4,5,6,9,10?

Divisibility Patterns819Is this number divisible by 2?

Divisibility Patterns819Is this number divisible by 2? No.

Divisibility Patterns819Is this number divisible by 2? No.Is this number divisible by 3?

Divisibility Patterns819Is this number divisible by 2? No.Is this number divisible by 3? Yes8 + 1 + 9 = 18, 1 + 8 = 9

Divisibility Patterns819Is this number divisible by 2? No.Is this number divisible by 3? YesIs this number divisible by 4?

Divisibility Patterns819Is this number divisible by 2? No.Is this number divisible by 3? YesIs this number divisible by 4? No.19 is not divisible by 4.

Divisibility Patterns819Is this number divisible by 2? No.Is this number divisible by 3? YesIs this number divisible by 4? No.Is this number divisible by 5?

Divisibility Patterns819Is this number divisible by 2? No.Is this number divisible by 3? YesIs this number divisible by 4? No.Is this number divisible by 5? NoThe last digit is not a 0 or 5.

Divisibility Patterns819Is this number divisible by 2? No.Is this number divisible by 3? YesIs this number divisible by 4? No.Is this number divisible by 5? NoIs this number divisible by 6?

Divisibility Patterns819Is this number divisible by 2? No.Is this number divisible by 3? YesIs this number divisible by 4? No.Is this number divisible by 5? NoIs this number divisible by 6? No

Divisibility Patterns819Is this number divisible by 9?

Divisibility Patterns819Is this number divisible by 9? Yes. 8 + 1 + 9 = 18

Divisibility Patterns819Is this number divisible by 9? No.

Divisibility Patterns819Is this number divisible by 9? No.Is this number divisible by 10?

Divisibility Patterns819Is this number divisible by 9? No.Is this number divisible by 10? No.

The last digit is not 0.

Divisibility PatternsAre all numbers that are divisible by nine also divisible by three?

Divisibility PatternsAre all numbers that are divisible by nine also divisible by three?

Yes, since nine is divisible by three.

But not all number that are divisible by three also divisible by nine.



4278 is divisible by 2, 3, and 6.

Divisibility Patterns30,135Is this number divisible by 2,3,4,5,6,9,10?

Divisibility Patterns30,135Is this number divisible by 2,3,4,5,6,9,10?

30135 is divisible by 3 and 5.



14980 is divisible by 2, 4, 5, and 10.

Divisibility Patterns16?7What digit can be placed in the ? for the entire number to be divisible by 3 ?

Divisibility Patterns16?7What digit can be placed in the ? for the entire number to be divisible by 3 ?1 + 6 +7 = 14; 1 + 4 = 5So ? can be either 1, 4, or 7


Divisibility Patterns4?5What digit can be placed in the ? for the entire number to be divisible by 4 ?None, there can never be a number that ends in 5 and is divisible by 4.


Divisibility Patterns54?66What digit can be placed in the ? for the entire number to be divisible by 6 ?5 + 4 +6 + 6 = 21; 2 + 1 = 3So ? can be either 0, 3, 6 or 9.

Divisibility PatternsAre all numbers that are divisible by ten also divisible by five?

Divisibility PatternsAre all numbers that are divisible by ten also divisible by five?

Yes, since ten is divisible by five. And it will also always be divisible by two.

Divisibility PatternsYou and three of your friends just won $4,567. Can you divide the money evenly?

Divisibility PatternsYou and three of your friends just won $4,567. Can you divide the money evenly?

you + 3 friends = 4

Since $4,567 is an odd number it can not be divisible by an even number.

Divisibility PatternsWas the year 1776 a leap year?


Since a leap (mostly) occurs every 4 years, is 1776 divisible by 4?

Since 76 is divisible by 4, then 1776 is also. 1776 was a leap year.




Since 22 is not divisible by 4, then 1922 is not. 1922 was not a leap year.

Divisibility PatternsWill the year 2054 be a leap year?

Divisibility PatternsWill the year 2054 be a leap year?


Since 54 is not divisible by 4, then 2054 is not. 2054 will not be a leap year.

Divisibility PatternsCindy needs to set up 252 chairs for a concert. She wants to put the same number of chairs in each row with no chairs left over. Can she put 6 chairs in each row?Divisibility PatternsCindy needs to set up 252 chairs for a concert. She wants to put the same number of chairs in each row with no chairs left over. Can she put 6 chairs in each row?

Yes, since 252 is an even number it is divisible by 2. Since 2 + 5 + 2 = 9 and 9 is divisible by three; 252 is divisible by 3. Since 252 is divisible by both 2 and 3, it is divisible by 6. Divisibility PatternsA T-shirt factory made 6,296 blue T-shirts. The factory put all the T-shirts into packages without any T-shirts left over. Can they fit the T-shirts in 4 packages?Divisibility PatternsA T-shirt factory made 6,296 blue T-shirts. The factory put all the T-shirts into packages without any T-shirts left over. Can they fit the T-shirts in 4 packages?

Yes, since 96 is divisible by 4, then 6,296 is divisible by 4. Divisibility PatternsA number is considered perfect if it is greater than 1 and the sum of its factors (not including the number) equals the number.

Divisibility PatternsA number is considered perfect if it is greater than 1 and the sum of its factors (not including the number) equals the number.For example;6 has factors of 1, 2 , 3 and 6;And 1 + 2 + 3 = 66 is called perfect.

Divisibility PatternsA number is considered perfect if it is greater than 1 and the sum of its factors (not including the number) equals the number.For example;6 has factors of 1, 2 , 3 and 6;And 1 + 2 + 3 = 66 is called perfect. Can you think of any other perfect numbers?

Divisibility PatternsA number is considered perfect if it is greater than 1 and the sum of its factors (not including the number) equals the number.

The next perfect number is 28. 28 has factors of 1, 2 , 4, 7, 14, 28;And 1 + 2 + 4 + 7 + 14 = 28

Divisibility PatternsFor the number ABC, each distinct letter represents a different digit. ABC, CAB, and BCA are all divisible by 6 and 9. What are the values of A, B, and C? Divisibility PatternsFor the number ABC, each distinct letter represents a different digit. ABC, CAB, and BCA are all divisible by 6 and 9. What are the values of A, B, and C?

Since each number is divisible by 2 (since it is divisible by 6), then the digits A, B and C must be even. Divisibility PatternsFor the number ABC, each distinct letter represents a different digit. ABC, CAB, and BCA are all divisible by 6 and 9. What are the values of A, B, and C?

Since it is divisible by 9, then A + B + C = 9What even number can be added together and get 9 ?Divisibility PatternsFor the number ABC, each distinct letter represents a different digit. ABC, CAB, and BCA are all divisible by 6 and 9. What are the values of A, B, and C?

4, 6, 8Divisibility PatternsAgenda NotesHomework Homework Practice R.4 Due Wednesday, Aug 26

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5 Minute Check Determine the missing digit to make the statement true. Complete on the back of your homework. 1. 1,376, ?59 is divisible by 3. 2. 1,376,