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Home >> Numbers >> Cube Numbers >> Properties of Cube Numbers >> Property 3 >>

If Natural Number has 3 at one's place, Cube Number of such Natural Number also has 7 at one's place

Property 1 Property 2 Property 3 Property 4 Property 5
Property 6 Property 7 Property 8 Property 9 Property 10
Property 11

Observe the following table:
Table 1
Natural Number Cube Number
1 1
2 8
3 27
4 64
5 125
6 216
7 343
8 512
9 729
10 1000
11 1331
12 1728
13 2197
14 2744
15 3375
16 4096
17 4913
18 5832
19 6859
20 8000
21 9261
22 10648
23 12167


Above table - 1 represents square of first 23 natural numbers.
You must have observed that the Natural Numbers having 3 at its one's place (highlighted in yellow) and their corresponding Cube Numbers have 7 at its one's place (highlighted in green).

i.e. Cube of 3 = 27
Cube of 13 = 2197
Cube of 23 = 12167

Let's try few more cube numbers as shown in table 2 and table 3:
Table : 2 Table : 3
Natural Number Cube Number
43 79507
44 85184
45 91125
46 97336
47 103823
48 110592
49 117649
50 125000
51 132651
52 140608
53 148877
54 157464
55 166375
56 175616
57 185193
58 195112
59 205379
60 216000
61 226981
62 238328
63 250047
Natural Number Cube Number
83 571787
84 592704
85 614125
86 636056
87 658503
88 681472
89 704969
90 729000
91 753571
92 778688
93 804357
94 830584
95 857375
96 884736
97 912673
98 941192
99 970299
100 1000000
101 1030301
102 1061208
103 1092727


Table - 2 represents cubes of numbers from 43 to 63
Table - 3 represents cubes of numbers from 83 to 103
In these tables also you will observe the same pattern which you observed in Table 1 i.e. Natural Numbers having 3 one's place (highlighted in yellow) and their corresponding cube Numbers have 7 at its one's place (highlighted in green).

So, this explains the property of square numbers that:
If a Natural Number has 3 at its one's place, then the Cube Number of such Natural Numbers always have 7 at its one's place.

Or we can also say that:
Cubes; of Natural Numbers ending with 3, end with 7.

Also we get that:
If a Natural Number has 7 at its one's place, then the Natural Number is not always a Perfect Cube.
e.g. 17, 67, 97 all are not cube numbers

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