*By Mr. Subramani K, Project Associate @IIITB*

Standard method is to multiplying 2, by 100 times that results:

1267650600228229401496703205376

Now, we have an interesting method of obtaining 2^100 without multiplication, which is explained as:

**Step 1: 2^10 (2 ^{10})**

- Write digit “1”, and add suffix “000”, then it becomes 1000
- Dividing the number by 50, 1000/50 =20
- Again, dividing by 5, 20/5 =4
- Then add all results: 1000 + 20 +4 =1024= 2^10 (2
^{10}) - Begin the next step with the result of this step.

**Step 2: 2^20 (2 ^{20})**

- Write digit “1024”, and add suffix “000”, then it becomes 1024000
- Dividing the number by 50, 1024000/50 =20480
- Again, dividing by 5, 20480/5 =4096
- Then add all results: 1024000 + 20480 +4096 =1048576= 2^20 (2
^{20})

Similarly,

**Step 3: **2^30 = 1073741824

**Step 4: **2^40 = 1099511627776

**Step 5: **2^50 = 1125899906842624

**Step 6: **2^60 = 1152921504606846976

**Step 7: **2^70 = 1180591620717411303424

**Step 8: **2^80 = 1208925819614629174706176

**Step 9: **2^90 = 1237940039285380274899124224

Begin the next step with the result of this step using the same logic.

**Step 10: **2^100 =

1237940039285380274899124224000

24758800785707605497982484480

4951760157141521099596496896

——————————————————-

1267650600228229401496703205376 = 2 ^ 100

We can conclude that the operation 2^{100}(2^100) can be performed without using any multiplication and only with the help of few additions and divisions.