Question

What is the hcf of 512,408,748long divison method

Answer 1

$\rm\bf\longrightarrow Factorisation \: of\: 512\\\\\begin{array}{r| l}2 & 521 \\ \cline{2-2} 2 & 256 \\ \cline{2-2} 2 &128 \\ \cline{2-2}2&64 \\ \cline{2-2} 2 & 32 \\ \cline{2-2} 2&16 \\ \cline{2-2} 2&8 \\ \cline{2-2} 2&4 \\ \cline{2-2} 2&2 \\ \cline{2-2}&1\end{array}$

$\rm \bf \longrightarrow Factorisation \: of \: 408\\\\\begin{array}{r | l} 2&408\\ \cline{2-2} 2&204\\ \cline{2-2} 2&102 \\ \cline{2-2}3&51 \\ \cline{2-2}17&17 \\ \cline{2-2}&1 \end{array}$

$\rm\bf\longrightarrow Factorisation \: of\: 748 \\\\\begin{array}{r | l} 2&748 \\ \cline{2-2} 2&374 \\ \cline{2-2} 11&187\\ \cline{2-2}17&17 \\ \cline{2-2}&1\end{array}$

$\rm Prime \:factorization \:of\: the\: numbers\: :$

$\rm 512 = 2\times2\times2\times2\times2\times2\times2\times2\times2 \\\\408 = 2\times2\times2\times3\times17\\\\748 = 2\times2\times11\times17$

$\underline{\rm \bf HCF = 2\times2 = 4}$