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 5
Examples: 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 3
Examples: 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)6408
quotient
• 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)6408
2)6408
2)6408
2)6408
3
32
320
3204
• 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
3
2 ) 7 12 1 8
36
2 ) 7 12 1 18
360
2 ) 7 12 1 18
3 609
• 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
Long Division compared to Shorthand Division
• 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:
436 , 029
2 872 , 058
8
07
6
12
 12
00
 0
04
 4
0
Shorthand Division:
(leave some space between the digits)
1
1
8 7 2, 0 5 8
2  4 3 6, 0 2 9
5
7
2 into 8 goes 4, exactly
2 into 7 goes 3, with 1 left over – making the next digit 12
2 into 12 goes 6, exactly
2 into 0 goes 0, exactly
2 into 5 goes 2, with 1 left over – making the next digit 18
2 into 18 goes 9, exactly
Long Division compared to Shorthand Division
• 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)
21 , 409
3 64 , 227
6
04
3
12
 12
02
 00
27
 27
0
1
2
6 4, 2 2 7
3  2 1, 4 0 9
2
4
3 into 6 goes 2, exactly
3 into 4 goes 1, with 1 left over – making the next digit 12
3 into 12 goes 4, exactly
3 into 2 goes 0, with 2 left over – making the next digit 27
3 into 27 goes 9, exactly