Euclid's Division Algorithm

What is an algorithm?

If the HCF of $657$ and $963$ is expressible in the form $657 x+963 \times \left(-15\right)$, find $x$.

Find the HCF of the following pairs of integers and express it as a linear combination of them.

$1288$ and $575$

If the linear combination is $575\times 9-1288\times k$, find the value of $k$?

If the HCF of $506$ and $1155$ can be expressed as a linear combination of them as $506\times k-1155\times 7$, then find the value of $k$.

If the $\mathrm{HCF}$ of $408$ and $1032$ is expressible in the form $1032 m-408\times 5$, find $m$.

Find the largest number which divides $615$ and $963$ leaving the remainder $6$ in each case.

Find the HCF of the following pair of integers and express it as a linear combination of them.

$595$ and $252$

If the linear combination is $252\times 26-595\times k$ , find the value of $k$ ?

Express the HCF of the following two numbers as a linear combination of them.

$963$ and $657$

If the linear combination is $657\times 22-963\times k$, find the value of $k$?

Use Euclid's division algorithm to find the HCF of $136, 170$ and $255$.

Find the HCF of $184, 230$ and $276$.

Use Euclid's division algorithm to find the HCF of $867$ and $255$.

Express the HCF of $468$ and $222$ as $468x+222y$ where $x,$ $y$ are integers in two different ways, and find the value of $x+y$.

A rectangular courtyard is $18 \mathrm{m} 72 \mathrm{cm}$ long and $13 \mathrm{m} 20 \mathrm{cm}$ broad. It is to be paved with square tiles of the same size. Find the least possible number of such tiles. (Write the numerical value as the final answer).

The length, breadth, and height of a room are $8 \mathrm{m} 25 \mathrm{cm},$ $6 \mathrm{m} 75 \mathrm{cm}$, and $4 \mathrm{m} 50 \mathrm{cm}$, respectively. The longest rod which can measure the three dimensions of the room exactly is $K cm$. Find the value of $K.$

$105$ goats, $140$ donkeys, and $175$ cows have to be taken across a river. There is only one boat which will have to make many trips in order to do so. The lazy boatman has his own conditions for transporting them. He insists that he will take the same number of animals in every trip, and they have to be of the same kind. He will naturally like to take the largest possible number each time. Can you tell how many animals went in each trip?

Find the HCF of $196$ and $38220$.

$15$ pastries and $12$ biscuit packets have been donated for a school feast. These are to be packed in several smaller identical boxes with the same number of pastries and biscuit packets in each. How many biscuit packets and how many pastries packets will each box contain? Find the total number of each type of packets in one box.

A mason has to fit a bathroom with square marble tiles of the largest possible size. The size of the bathroom is $10 \mathrm{ft}.$ by $8 \mathrm{ft}.$ How many tiles are required if the size in inches of the tile required has to be cut? 

Two brands of chocolates are available in packs of $24$ and $15$, respectively. If I need to buy an equal number of chocolates of both kinds, what is the least number of boxes of each kind I would need to buy? Write the sum of total number of boxes as final answer.

Using Euclid's division algorithm, find the largest number that divides $1251,9377$ and $15628$ leaving remainders $1,2$ and $3$ respectively.