Question

Let's make a grid and find out the prime numbers in between

1

and

200

by the Sieve of Eratosthenes method.

Accepted Answer

We know that,

The numbers which have only $2$ factors i.e., $1$ and the number itself are called prime numbers, and the numbers which have factors other than $1$ and itself are called composite numbers.

From the given,

We are asked to write the prime numbers between $1$ and $200$ .

So, let's start creating the grid.

1. First, let's strike out 1 with ' $1$ ' as 1 is neither prime nor composite.
2. Next, let's ' $2$ ' like this and strike out the other multiples of $2$ , that is, $4, 6, 8 . . .$ with ' $/$ '.
3. We see that the number next to $2$ , which has not been struck out is $3$ . Let's circle 3 like ' $3$ ' and strike out the other multiples of $3$ , that is, $6, 9, 12 . . .$ with ' $/$ '.
4. We see that the number next to $3$ , which has not been struck out is $5$ . Let's circle 5 like ' $5$ ' and strike out the other multiples of $5$ , that is, $10, 15, 20 . . .$ with ' $/$ '.
5. We repeat this process until all numbers of the grid are circled like this ' $n$ ' or struck out with this ' $/$ '.

$1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$

$11$ $12$ $13$ $14$ $15$ $16$ $17$ $18$ $19$ $20$

$21$ $22$ $23$ $24$ $25$ $26$ $27$ $28$ $29$ $30$

$31$ $32$ $33$ $34$ $35$ $36$ $37$ $38$ $39$ $40$

$41$ $42$ $43$ $44$ $45$ $46$ $47$ $48$ $49$ $50$

$51$ $52$ $53$ $54$ $55$ $56$ $57$ $58$ $59$ $60$

$61$ $62$ $63$ $64$ $65$ $66$ $67$ $68$ $69$ $70$

$71$ $72$ $73$ $74$ $75$ $76$ $77$ $78$ $79$ $80$

$81$ $82$ $83$ $84$ $85$ $86$ $87$ $88$ $89$ $90$

$91$ $92$ $93$ $94$ $95$ $96$ $97$ $98$ $99$ $100$

$101$ $102$ $103$ $104$ $105$ $106$ $107$ $108$ $109$ $110$

$111$ $112$ $113$ $114$ $115$ $116$ $117$ $118$ $119$ $120$

$121$ $122$ $123$ $124$ $125$ $126$ $127$ $128$ $129$ $130$

$131$ $132$ $133$ $134$ $135$ $136$ $137$ $138$ $139$ $140$

$141$ $142$ $143$ $144$ $145$ $146$ $147$ $148$ $149$ $150$

$151$ $152$ $153$ $154$ $155$ $156$ $157$ $158$ $159$ $160$

$161$ $162$ $163$ $164$ $165$ $166$ $167$ $168$ $169$ $170$

$171$ $172$ $173$ $174$ $175$ $176$ $177$ $178$ $179$ $180$

$181$ $182$ $183$ $184$ $185$ $186$ $187$ $188$ $189$ $190$

$191$ $192$ $193$ $194$ $195$ $196$ $197$ $198$ $199$ $200$

In Sieve of Eratosthenes method, numbers circled with' $n$ ' way are prime numbers and all the numbers struck out like this ' $n$ ' are composite numbers.

Therefore, the required answer is given above.

Let's make a grid and find out the prime numbers in between $1$ and $200$ by the Sieve of Eratosthenes method.

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