Number Theory Review

Factors of 42

1 x 42

2 x 21

3 x 14

6 x 7

This is a sequence of prime numbers.

This is a sequence of square numbers

6 x 6 = 36

7 x 7 = 49

Square root of 144 = 12

This is a sequence of cubed numbers

3 x 3 x 3 = 27

6 x 6 x 6 = 216

Cube root of 729 = 9

$$\sqrt[]{555}=\ 23.5584379788$$  

$$5^2=25$$  

$$2^3=8$$  

$$\sqrt[3]{222\ =}6.05504894651$$  

(23.56 + 25)/ (8 x 6.05)

48.56/48.4 = 1.003

$$2^{8\div2}=2^4$$  

$$3^{4\div2}=3^2$$  

$$5^{2\div2}=\ 5$$  

$$2^4\times3^2\times5=720$$  

or

$$\sqrt[]{2\times2\times2\times2\times2\times2\times2\times2\times3\times3\times3\times3\times5\times5}$$  

$$2^{6\ \div3}=2^2$$  

$$7^{3\div3}=7$$  

$$2^2\times7=28$$  

or $$\sqrt[3]{2\times2\times2\times2\times2\times2\times7\times7\times7}$$  

$$3136\ =\ 2^6\times7^2$$  

$$\sqrt[]{2^6\times7^2}=2^{3\ }\times\ 7\ =\ 56$$   $$\sqrt[]{2\times2\times2\times2\times2\times2\times7\times7}$$