MrV’s Shorthand Division(by Single Digits 2, 5, and 3)

It Helps You Do Prime Factorization using Factor Trees:

If you are SURE that a long number divides exactly by 2, 5, or 3, you can use Shorthand Division to quickly find the other factor.

Easy Tests for Divisibility:2: Only even numbers (ending with 0, 2, 4, 6, or 8) divide by 2

Examples: 34,138 will divide by 2, but 123,243 will not

5: Only numbers ending with 0 or 5 will divide by 5Examples: 3,005 will divide by 5, but 3,002 will not

3: Only numbers with a digit sum that divides by 3 also divide by 3Examples: 15,201 will divide by 3, but 15,202 will not 1+5+2+0+1=9 1+5+2+0+2=10

7: There’s no easy test - Divide by 7 (use either kind of division) to see if you get a 0 remainder

4, 6, 8, and 9: Why bother? Check for the primes first. If 2 and 3 will not divide, then these other digits will not

How to do Shorthand Division• Let’s use 6408 divided by 2 as an example…• Write the division with the division symbol upside down,

and build the quotient underneath it --> 2 ) 6 4 0 8 • Work left to right, one digit at a time

2 into 6 is 3 2 into 4 is 2 2 into 0 is 0 2 into 8 is 4 2 ) 6 4 0 8 2 ) 6 4 0 8 2 ) 6 4 0 8 2 ) 6 4 0 8 3 3 2 3 2 0 3 2 0 4

• It’s easy if each little division goes evenly. But if not… ?• Let’s call any remainders “carries.” (They get carried to the next digit)

2 into 7 is 3, r1 2 into 12 is 6 2 into 1 is 0 r1 2 into 18 is 9 2 ) 7

12 1 8 2 ) 7 12 1 8 2 ) 7

12 1 18 2 ) 7

12 1 18

3 3 6 3 6 0 3 6 0 9• Many students can do these little divisions in their heads, but

some may find MrV’s Tables are useful when dividing by 3, 5 and 7

quotient

• Dividing a number by 2: Either it goes exactly, or there is a remainder of 1

• You can use MrV’s Times Table. You may find it easier if you do some computations in your head

• Long Division: Shorthand Division: (leave some space between the digits)

920,6342

850,278 11

Long Division compared to Shorthand Division

029,436058,8722

807621120000440

75

2 into 8 goes 4, exactly2 into 7 goes 3, with 1 left over – making the next digit 122 into 12 goes 6, exactly2 into 0 goes 0, exactly2 into 5 goes 2, with 1 left over – making the next digit 182 into 18 goes 9, exactly

• Dividing a number by 3: Either it goes exactly, or there is a remainder of 1 or 2

• You can use MrV’s Times Table. You may find it easier if you do some computations in your head

• Long Division: Shorthand Division: (leave some space between the digits)

904,123

722,46 21

Long Division compared to Shorthand Division

409,21227,643

60432112020027270

42

3 into 6 goes 2, exactly3 into 4 goes 1, with 1 left over – making the next digit 123 into 12 goes 4, exactly3 into 2 goes 0, with 2 left over – making the next digit 273 into 27 goes 9, exactly