dividing large numbers

Mar 2010
4
0
First I will write this example in European notation ( I hope you will understand ).
Lets say I am dividing 41472 / 324 = 128.
I' am doing this like that:
41472 / 324 = 128 // 414 / 324 = 1 remainder 90
907 // write 90 and 7, 907 / 324 = 2 remainder 259
2592 // write 259 and 2, 2592 / 324 = 8 remainder 0

Is there anyway to do divison mechanically (like multiplication)? For example, in last step when I am dividing 2592 / 324 = 8, I need to guess in my head that 324 goes 8 times in 2592.
 

Prove It

MHF Helper
Aug 2008
12,883
4,999
First I will write this example in European notation ( I hope you will understand ).
Lets say I am dividing 41472 / 324 = 128.
I' am doing this like that:
41472 / 324 = 128 // 414 / 324 = 1 remainder 90
907 // write 90 and 7, 907 / 324 = 2 remainder 259
2592 // write 259 and 2, 2592 / 324 = 8 remainder 0

Is there anyway to do divison mechanically (like multiplication)? For example, in last step when I am dividing 2592 / 324 = 8, I need to guess in my head that 324 goes 8 times in 2592.
Find common factors in the numerator and denominator and divide numerator and denominator by those factors.
 
Mar 2010
4
0
I see
2592 = 3*3*3*3*2*2*2*2*2*2
324 = 3*3*3*3*2*2
so 2592/324 = 2*2*2

Guess that is only way.
 

Prove It

MHF Helper
Aug 2008
12,883
4,999
I see
2592 = 3*3*3*3*2*2*2*2*2*2
324 = 3*3*3*3*2*2
so 2592/324 = 2*2*2

Guess that is only way.
Actually it's \(\displaystyle 2\cdot 2\cdot 2 \cdot 2\).