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Home >> Numbers >> Cube Numbers >> Properties of Cube Numbers >> Property 4 >> If Natural Number has 4 at one's place, Cube Number of such Natural Number also has 4 at one's place
Observe the following table:
Table 1
Natural Number | Cube Number |
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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 | 24 | 13824 |
Above table - 1 represents square of first 24 natural numbers.
You must have observed that the Natural Numbers having 4 at its one's place (highlighted in yellow) and their corresponding Cube Numbers also have 4 at its one's place (highlighted in green).
i.e. Cube of 4 = 64
Cube of 14 = 2744
Cube of 24 = 13824
Let's try few more cube numbers as shown in table 2 and table 3:
Table : 2 | Table : 3 |
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Natural Number | Cube Number |
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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 | 64 | 262144 |
| Natural Number | Cube Number |
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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 | 104 | 1124864 |
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Table - 2 represents cubes of numbers from 44 to 64
Table - 3 represents cubes of numbers from 84 to 104
In these tables also you will observe the same pattern which you observed in Table 1 i.e. Natural Numbers having 4 one's place (highlighted in yellow) and their corresponding cube Numbers also have 4 at its one's place (highlighted in green).
So, this explains the property of square numbers that:
If a Natural Number has 4 at its one's place, then the Cube Number of such Natural Numbers always have 4 at its one's place.
Or we can also say that:
Cubes; of Natural Numbers ending with 4, also end with 4.
Also we get that:
If a Natural Number has 4 at its one's place, then the Natural Number is not always a Perfect Cube.
e.g. 24, 64, 94 all are not cube numbers
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