Question Number 55476 by pooja24 last updated on 25/Feb/19
$$\mathrm{4}\:{metal}\:{rods}\:{of}\:{length}\:\mathrm{78}\:{cm},\mathrm{104}\:{cm},\mathrm{117}{cm}, \\ $$$${a}.{nd}\:\mathrm{169}\:{cm}\:{are}\:{to}\:{be}\:{cut}\:{into}\:{parts}\:{of}\:{equal}\:{length} \\ $$$${Each}\:{length}\:{must}\:{be}\:{as}\:{long}\:{as}\:{possible} \\ $$$${What}\:{is}\:{the}\:{maximum}\:{number}\:{of}\:{pieces} \\ $$$${that}\:{can}\:{be}\:{cut}? \\ $$
Answered by Joel578 last updated on 25/Feb/19
$$\mathrm{GCD}\left(\mathrm{78},\:\mathrm{104},\:\mathrm{117},\mathrm{169}\right)\:=\:\mathrm{13} \\ $$$$\mathrm{Number}\:\mathrm{of}\:\mathrm{pieces}\:=\:\frac{\mathrm{78}}{\mathrm{13}}\:+\:\frac{\mathrm{104}}{\mathrm{13}}\:+\:\frac{\mathrm{117}}{\mathrm{13}}\:+\:\frac{\mathrm{169}}{\mathrm{13}}\:=\:\mathrm{36} \\ $$
Commented by tanmay.chaudhury50@gmail.com last updated on 25/Feb/19
$${excellent}…{confidance}\:{enhance}\:{determination}… \\ $$
Commented by Joel578 last updated on 25/Feb/19
$${thanks}\:{sir} \\ $$