How To multiply numbers with large exponents

How to find factors with large numbers

So you have 3^16 power?

Well… that is 3*3*3*3*3*3*3*3*3*3*3*3*3*3*3*3

3*3 = 9…

So then you can group the 3’s together.

(3*3)*(3*3)*(3*3)*(3*3)*(3*3)*(3*3)*(3*3)*(3*3)

That gives you… 9*9*9*9*9*9*9*9 (or in other words, 9^8)

9*9=81, or (9*9)*(9*9)*(9*9)*(9*9)*(9*9)

81^4=9^8=3^16

The shortcut is easy – Square the number and half the exponent!

2 to the 104th power is also

4 to the 52th and

16 to the 26th.

256 to the 13th

1.

everything is divisible by 1

2.

for the number 2, if it ends in 0,2,4,6, or 8, it is divisible by 2 evenly

3.

for the number 3, take all the digits in a number and if it is divisible by 3evenly

you can evenly divide it by 3

ex. 456= 4+5+6=15 and 15= 1+5+6 and you can divide 6 by 3

4.

if the last 2 digits are divisible by 4 so is the whole number

ex. 394856378945024 the last 2 numbers are 24 and you can divide 24 by 4 so

394856378945024 is divisible by 4

5.

if the number ends in 5 or 0 you can divide it by 5

6.

if the number can be divided by 2 and 3, you can divide it by 6 evenly

7.

7 has no short cut sorry…

8.

if the last 3 digits are divisible by 8 so is the whole number

ex. 394856378945o24 the last 3 digits are 024 and 24 is divisible by 8 so

394856378945024 is divisible by 8

9.

take all the digits of a number and add them, if you can divide it by 9 it is divisible by 9

ex. 381= 3+8+1=12 12= 1+2=3 no! but 963= 9+6+3=18 18= 1+8=9 yes! so 963,936,693,639,396,369

are all divisible by 9

10.

if it ends in 0, it is divisible by 10

11.

take 11*5678 5+6+7+8=26 so add 26 to the middle (note any number over nine carries over

carries over)so 58678

12.

if 3 and 4 go into it, then so doe 12

14.

if 2 and 7 go into it, so does 14

15.

is 3 and 5 go into it, so does 15

all other numbers…

take the number and find 2 factors that do not go into each other

ex. 60) if 2 and 30 go into it it does not mean 60 will because you can divide 30 by 2

ex. 60) if 20 and 3 go into it is does go into 60 because 20 is not divisible by 3