Division as repeated subtraction - introduction to long division
Free lesson plan from HomeschoolMath.net

 
It just takes quite a long time, doesn't it?  Instead you can take a 'shortcut' and initially subtract 300 apples (taking 100 bags) or some other big multiple of 3.
 

 Let's figure it out and keep count of the bags as we subtract (put in bags) the apples. 
 

Method 1 - slower Apples Bags 771 - 300 471 100 bags - 300 171 100 bags - 30 141 10 bags - 30 111 10 bags - 30 81 10 bags - 30 51 10 bags - 30 21 10 bags - 21 0 7 bags

Method 2 - quicker  Apples Bags 771 -  600 200 bags 171 -  150 50 bags 21 7 bags -  21 0

It's over 700 apples. In 100 bags would have 300 apples. In 200 bags would have 600 apples. In 300 bags would have 900 apples; too many bags.  Subtracting the 600 apples from 771 leaves 171 still  to be bagged. It's over 170 apples still. In 10 bags I'll have 30 apples. In 20 bags I'd have 60 apples. In 50 bags I'd have 150 apples. In 60 bags I'd have 180 apples; that's too many.  Subtract 150 apples from 171; 21 apples are left.  Need 7 bags for the last 21 apples.

 
So total needed 200 + 50 + 7 = 257 bags to bag all the apples.  And it all went even - no apples
left over!  In other words, 771 ÷ 3 = 257.

Example 5.  It won't matter even if you do the subtracting in smaller steps.  Compare the two ways
to do the division 795 ÷ 3  by subtracting repeatedly.  You can think in terms of bagging apples if it helps.

Dividend Quotient 795 -  300 100 495 - 300 100 195  - 30 10 165 - 30 10 135 - 30 10 105

Dividend Quotient 795 -  600 200 195 - 180 60 15 -  15 5 0

So total the quotient is _____ + ___  + ___ = _____, and division is even.   In other words, 795 ÷ 3 = ______.