1. Cube and its properties

2. Property 1 If a number end with 1, then its cube will also end with 1
Example:
Numbers
One’s Place
Rule
Answer 1
number end with 1
Cube of 51 will end with 1 51 1
number end with 1
Cube of 121 will end with 1
121
191 1
number end with 1
Cube of 191 will end with 1
23571 1
number end with 1
Cube of will end with 1

3. Cubes of an even numbers are all even numbers
Property 5
Observe the following table
Number
Square
Number
Square
Cubes of an even numbers are all even numbers 2 8 1 1 3 27 4 64 5
125 6
216
Cubes of odd numbers
are all odd numbers 7
343 8
512 9
729 10
1000

4. Property 2
If a number ends with 0 , 1 , 4 , 5 , 6 and 9 , then its cube will end with same number
For Example:
Numbers
One’s Place
Rule
Answer 11 1
number ends with 0 , 1 , 4 , 5 , 6 and 9
Cube of 11 will end with 1 14 4
number ends with 0 , 1 , 4 , 5 , 6 and 9
Cube of 14 will end with 4 15 5
number ends with 0 , 1 , 4 , 5 , 6 and 9
Cube of 15 will end with 5 16 6
number ends with 0 , 1 , 4 , 5 , 6 and 9
Cube of 16 will end with 6 20
number ends with 0 , 1 , 4 , 5 , 6 and 9
Cube of 20 will end with 0 19 9
number ends with 0 , 1 , 4 , 5 , 6 and 9
Cube of 19 will end with 9

5. Property 3 If a number end with 2, then its cube will end with 8
For Example:
Numbers
One’s place
Rule
Answer 12 2
Number ends with 2
Cube of 12 will end with 8 18 8
Number ends with 8
Cube of 8 will end with 2

6. Property 4 If a number end with 3, then its cube will end with 7
For Example:
Numbers
Ones place
Rule
Answer 13 3
number end with 3
cube of 13 will end with 7 17 7
number end with 7
cube of 17 will end with 3

7. Try These
By observing the units digits find which of the numbers cannot be a perfect cube 2321 , 1335 , , , , 4173.