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Long Division Method


While learnermath.com does assume that visitors will have a prior understanding of division in Math.

The long division method is an approach to larger division sums that is worthwhile demonstrating here.
Long division is something that seems to intimidate quite a few people initially, but it really doesn’t turn out to be as tricky as some would believe.

We’ll show the steps involved in using the long division method, which can be applied to many large division sums when required.




Long Division Method Examples



(1.1) 

864 ÷ 16

Solution   


1)  The first step here in using the long division method is to set the numbers up like we would with a short division sum.

16  864

For the first bit of division, 16 doesn’t go into 8, so we put a 0 above in the solution section.
       0
16  864


But now 16 does go into 86. At this stage we ignore any remainders from division, in which case 16 goes into 86 five times.
       05
16  864




2)  Next we multiply 16 by this 5.     16 × 5 = 80
      We then place this number below 86 in the dividend, subtract, then place the result below.

       05
16  864
   
80
         6



3)   Now the next number in the dividend in brought down alongside the  6.
      Here this is  4,  so we will have  64.

       05
16  864
   
80
         64


This  64  is now divided by  16,  and the result is placed appropriately above in the answer.     64 ÷ 16 = 4
       054
16  864
   
80
         64



4)   Then it’s the same process again, this  4  from the answer is multiplied by our divisor  16.
        Followed by being subtracted from the number above.

       054
16  864
   
80
         64
     
64
           0



The result is  0,  and with no numbers in the dividend left to bring down, the long division method is complete.
With no remainder in the answer.

864 ÷ 16  =  54





(1.2) 

658 ÷ 12 ?

Solution   


1)

12  658

Firstly,  12  doesn’t go into  6,  so we put a  0  above.
       0
16  864


But ignoring remainders,  12  does go into  65  five times.
       05
12  658




2)   Next we multiply  12  by the  5.     12 × 5 = 60
      We then place this number below 65 in the dividend, subtract, then place the result below.

       05
12  658
   
60
         5



3)     The next number in the dividend can now be brought down alongside the  6,  giving us  58.

       05
12  658
   
60
         58


This  58,  again ignoring remainders, can now be divided by  12,  with the result is placed appropriately above in the answer.
58 ÷ 12 = 4
       054
12  658
   
60
         58



4)     Now using same process again, this  4  from the answer is multiplied by the divisor  12.
        Followed by being subtracted from the number above.

       054
12  864
   
60
         58
     
48
         10



The result of this is  10,  and now with no numbers in the dividend left to bring down, the long division method is complete.
With the remaining  10  below, being the remainder in the answer.

658 ÷ 12  =  54 remainder 10





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