| 10. | What is the least number of squares tiles required to pave the floor of a room 15 m 17 cm long and 9 m 2 cm broad? |
| [A]. | 814 | | [B]. | 820 | | [C]. | 840 | | [D]. | 844 | Answer: Option A Explanation: Length of largest tile = H.C.F. of 1517 cm and 902 cm = 41 cm. Area of each tile = (41 x 41) cm2.  Required number of tiles = |  | 1517 x 902 |  | = 814. | | 41 x 41 | |
| Idk said: (Sep 10, 2010) | |
| Can anyone explain the logic why HCF is used ? |
| Divya said: (Oct 2, 2010) | |
| Why HCF is used? |
| Shanthi said: (Oct 23, 2010) | |
| Length and breath are given. So area of rectangle is lxb. Also they are askin to find the least no. of square tiles. For square tiles we need the area. In a square al the sides are equal. Hcf is the highest common factor of 1517 and 902. So 41 is the hcf n area of square is 41^2. So divide area of rect by area of square. |
| Vivek Jain said: (Jul 1, 2011) | |
| Hi divya! I am also not getting why hcf is used. If you have got the answer then reply me please. |
| Shashank said: (Aug 8, 2011) | |
| Since hcf is a prime no. , how we can find the hcf of such big numbers. For those who want to know why hcf::. As we have to set square tiles in a rect. Floor that's why we need a comman factor for both length and breadth so that the no. Of tiles is a natural number but not a fraction! |
| Vinod Mishra said: (Aug 13, 2011) | |
| Hi I m not getting the hcf of 1517 and 902 is 41. How it has calculated ? |
| Ibrahimsha said: (Sep 29, 2011) | |
902)1517(1
902
------
615)902(1
615
---
287)615(2
574
---
41)287(7
287
---
0 By this method of successful division, remainder goes 0. Last divisor forms your req. HCF.... So 41 is ur HCF :-) |
| Sara said: (Oct 15, 2011) | |
| Why we require hcf here? |
| Balajisingh said: (Jan 10, 2012) | |
| Imbrhimsha now I'm clear with HCF thank you. |
| Vani Varma said: (Feb 7, 2012) | |
| Thank you shanthi, shasank and Ibrahimsha. |
| Hardik said: (Aug 23, 2012) | |
| Please explain all steps. |
| Shashi said: (Mar 5, 2013) | |
| To calculate least no.of square we need largest tiles so that it can cover it in less no of tiles so we need a highest number out of (1517 & 902) which can divide the area entirely and it can only be obtained by HCF. |
| Sumi said: (Mar 24, 2013) | |
| @Shashi. Well said. To calculate least no.of square we need largest tiles. That means we need to have highest common factor for 1517 & 902. |
| Pradeep said: (Mar 31, 2013) | |
| The highest no that can divide both length and breadth so that the tiles used can occupy all the available space exactly. |
| Suparna said: (Jun 5, 2013) | |
| Is there any other easy method to calculate HCF? |
| Koushik Kallamadi said: (Jul 31, 2013) | |
| Hi friends, We can also use the dimensions (9.02*9.02) + (6.15*6.15) +2(2.87*2.87) +7(0.41*0.41) and totally 11 square tiles of different lengths. |
| Valli said: (Dec 4, 2013) | |
| What's the reason about using hcf? |
| Apurv said: (Dec 19, 2013) | |
| Least no of square tiles. Mean largest tiles. |
| Faraz said: (Jul 21, 2014) | |
| Here they are telling least number of square tiles not least area of square tile, so we need big tile thats why hcf otherwise we take lcm. I hope you understand least number of tile. |
| Anbarasu said: (Aug 22, 2014) | |
| What is the reason about using hcf? |
| Praveen said: (Apr 15, 2015) | |
| I'm can't understand please explain. How to get the value 41 from the HCF? |
| Sukumar Satyen said: (Jun 22, 2015) | |
| For same type of Questions, we can also use different formula: Number of Squares inside Rectangle: = Square of (LCM of Length and Width of Rectangle)/(Area of Rectangle). = (33374*33374)/(1517*902) = 814. |
| Abc said: (Jul 24, 2015) | |
| I am unable to find the LCM I tried it a lot can you give me a guess how did it come? |
| Sheetal said: (Aug 3, 2015) | |
| I couldn't understand why HCF is taken? |
| Suresh said: (Aug 28, 2015) | |
| Friends HCF have taken because we need square tiles, so we need to divide length and breadth of floor in equal parts, that's why we are taking HCF. |
| Isha said: (Oct 2, 2015) | |
| Hey where did we get 1517 and 902 from? |
| Bhavna said: (Oct 16, 2015) | |
| We are converting metres to centimetres. |
| Narayanan said: (Mar 25, 2016) | |
| The least number is asked that means a single tile with the maximum dimension. For this try LCM , you will get the maximum number of tiles with minimum dimensions whereas, in HCF, you will get the largest dimension possible. So that only HCF is used to find the answer. |
| Abdullah Akhtar said: (Apr 23, 2016) | |
| @Narayanan. Thanks for explaining it. |
| Jhanvi said: (May 31, 2016) | |
| How you got 1517 and 902? Please explain. |
| Anoop said: (Jun 9, 2016) | |
| @Suresh. Thank you for explaining why HCF is used here.. |
| Pink_Love said: (Jul 9, 2016) | |
| @Jhanvi. In the question, one length is given in cm and another in m. So we have to convert m into cm.
i.e 15m=15 * 100cm (same for the breadth). And for HCF. 1517 = 37 * 41,
902 = 22 * 41, So HCF = 41,
Area = 41 * 41,
Req no of tiles = 1517 * 902/41 * 41 = 814. |
| Ramesh said: (Jul 28, 2016) | |
| I didn't understand the Last step multiplication. Someone help me. |
| Abhi said: (Aug 1, 2016) | |
| Please tell me how many tiles will be used in that room whose length or breath is 20 m and 16 cm or 15 m 60 cm. |
| Sathyaraj K said: (Sep 13, 2016) | |
| Thank you @Ibrahimsha. |
| Shridhar said: (Sep 27, 2016) | |
| Thank you for your solution @Ibrahimsha. |
| Vinay said: (Nov 26, 2016) | |
| Why squares need to be of same size? |
| S. Nipin said: (Feb 16, 2017) | |
| Suppose if the question was asked to find maximum no. of tiles then how to find the answer? |
| Anuj Chhetri said: (Mar 17, 2017) | |
| We need that size of square which must occupy the entire space. If we take side of some other square, then 100% some space gona left as we can't bread the last tile. If we take the hcf, then we can get the side of square which is divisible by length and breadth both exactly. |
| Naqi Zaidi said: (Mar 27, 2017) | |
| HCF of any two or more numbers tells the highest possible no that can divide all the numbers. Since the question asks the minimum no of tiles, so it means you need a maximum possible size of the tile. Which will ensure minimum no of tiles? If the question says that maximum tiles then you will calculate LCM. |
| Soniya said: (Apr 22, 2017) | |
| Why hcf is taken? Please explain. |
| Anc said: (Apr 27, 2017) | |
| Where does the 1517comes from? |
| Arpan Jadhao said: (May 17, 2017) | |
| How 1517 comes from? I didn't understand it. Please explain me. |
| Richa said: (May 26, 2017) | |
| Thanks @Ibrahimsha. |
| Rohit said: (Jun 1, 2017) | |
| HCF is taken because we want the least no.of tiles in this question. If we want least no of tiles then we have to maximise the dimensions of tiles. So HCF (Higher Common Factor) is used to maximise the dimensions of tiles. |
| Tina said: (Jun 24, 2017) | |
| I am not getting the solution properly. Please, could anyone explain me? |
| Siddharth said: (Jul 4, 2017) | |
| @Tina. The dimensions of the room is 1517cm X 902cm.
Square tiles of the same side are only to be used. So dimensions of the square tiles should not be in integral metres. Since no. of square tiles to be paved are whole numbers, 1517 and 902 should be divisible by a number which gives the number of square tiles to be paved along length and breadth.
Thus hcf is used.
Area of room / Area of 1 tile = No. of tiles.
= ( 1517 X 902 ) / ( 41 X 41 ) = 37 X 22 = 814 tiles. |
| Roop said: (Jul 22, 2017) | |
| Hcf is calculated because for least tiles we need area of the square be maximum. |
| Bhavishya said: (Oct 4, 2017) | |
| Thank you so much for the explanation. |
| Srivalli said: (Dec 8, 2017) | |
1m=100 Cms, so convert 15meters *100=1500+17cms=1571,
Like wise 9meters*100=900+2cms=902cms. |
| Sakshi said: (Jan 10, 2018) | |
| Thank you @Srivalli. |
| Harish said: (Oct 3, 2018) | |
| Here 41 * 37=1517 and 41 * 22=902. So, 41 comes in both the no. (which is called hcf).
Now the area of the floor is 1512 * 902.
So least no. of tiles to cover the floor = n * 41^2 (as square tile can be taken of length 41).
Therefore n =37*22 =814. |
| Richy said: (Oct 6, 2018) | |
| @All. If we want to get the least number of tiles, the largest tiles must be used. This is why hcf is used. If you want to get the most number of tiles, then, the smallest tiles will be used, which is lcm. |
| Shekarreddy said: (Jan 27, 2019) | |
| Why we use HCF here? |
| Raghuvansh said: (Jul 1, 2019) | |
| Thanks for your explanation of HCF @Ibrahimsha. |
| Sudarshan Jain said: (Jan 12, 2020) | |
| Thanks all. |
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What Is the Least Number of Square Tiles
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