Question

using Euclids algorithm find the largest number which divides 870 and 258 leaving remainder 3 in each case​

Answer 1

$\textbf{Given numbers are 870 and 258}$

$\text{We have to find the largest number which divides 870}$

$\text{and 258 leaving remainder 3}$

$\text{It is enough to find the HCF of 867 and 255}$

$\begin{array}{r|l}&3\\\cline{2-2}255&867\\&765\\\cline{2-2}&\;102\end{array}$

$\begin{array}{r|l}&2\\\cline{2-2}102&255\\&204\\\cline{2-2}&\;51\end{array}$

$\begin{array}{r|l}&2\\\cline{2-2}51&102\\&102\\\cline{2-2}&\;\;0\end{array}$

$\text{In the last division, we get the remainder 0}$

$\implies\textbf{HCF of 867 and 255 is 51}$

$\therefore\textbf{51 is the required number which divides 870 and 258}$

$\textbf{leaving remainder 3}$

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Answer 2

Given:

divides 870 and 258

leaving remainder 3

To find:

find the largest value by Euclids algorithm

Solution:

Given value:

⇒870 and 258

If we remove 3 from the given value it will give:

$\to 870-3 =867\\\\\to 258-3=255$

divides the value by Euclid's algorithm:

⇒867 ÷ 255 = 3 R 102    (867 = 3 × 255 + 102)

⇒255 ÷ 102 = 2 R 51    (255 = 2 × 102 + 51)

⇒102 ÷ 51 = 2 R 0    (102 = 2 × 51 + 0)

The remainder value is 0, and the last equation that is GCF = 51