Question

Can you divide the number 8,101,265,822,784 by 8 without using either long or short division?

Answer 1

If I couldn't use long division or short division, I would use the calculator with the total of 1.0126582e+12

Answer 2

Yes. If we wanted to divide 104 by 8 we could write 104 as sum of multiples of 8 with which we are familiar:

104=80+24

then
`(104)/(8)= (80+24)/(8)= (80)/(8)+ (24)/(8)=10+3=13`

We use the same procedure to divide the given number by 8:



First We can "decompose" the number as a sum of multiples of 8 which we recognize easily. Then, divide each single one of them with 8.

That is

8,101,265,822,784 = 8,000,000,000,000+100,000,000,000+1,000,000,000

+265,822,784

now decompose 265,822,784:

265,822,784=240,000,000+24,000,000+1,000,000+800,000+22,784

now decompose 22,784

22,784=16,000+6,784

decompose 6,784

6,784=6,400+384= 6,400+320+64


Thus:

8,101,265,822,784 : 8 =(8,000,000,000,000+100,000,000,000+1,000,000,000+240,000,000
+24,000,000+1,000,000+800,000+16,000+6,400+320+64):8

=1,000,000,000,000+12,500,000,000+125,000,000+30,000,000+
3,000,000+125,000+100,000+2,000+800+40+8

=(1,000,000,000,000+12,500,000,000)+(125,000,000+30,000,000)
+ 3,227,848

=1,012,500,000,000+155,000,000+3,227,848

=1,012,655,000,000+3,227,848

=1,012,658,227,848