Findnumber whichthegreatestgreatestpossiblepossi960 and 1can divide 17

1.	Findnumber whichthegreatestgreatestpossiblepossi960 and 1can divide 176, 1152. andin each ease;remainder w same in near
Answer» Suppose the greatest number which can divide 76, 132 and 160 ispand the remainder isr. Also letq1,q2andq3are the quotients of 76, 132 and 160 respectively. So we have; pq1+r=76...(i)pq2+r=132...(ii)pq3+r=160...(iii) Nowfrom(i),(ii)and(iii)weget;p(q2−q1)=132−76=56p(q3−q2)=160−132=28p(q3−q1)=160−76=84 Therefore HCF of 56, 28 and 84 is given by; 56=2×2×2×728=2×2×784=2×2×3×7 HCFOF56,38and84=2×2×7=28Therefore the required greatest number is 28

Findnumber whichthegreatestgreatestpossiblepossi960 and 1can divide 176, 1152. andin each ease;remainder w same in near

Answer»

Suppose the greatest number which can divide 76, 132 and 160 ispand the remainder isr.

Also letq1,q2andq3are the quotients of 76, 132 and 160 respectively.

So we have;

pq1+r=76...(i)pq2+r=132...(ii)pq3+r=160...(iii)

Nowfrom(i),(ii)and(iii)weget;p(q2−q1)=132−76=56p(q3−q2)=160−132=28p(q3−q1)=160−76=84

Therefore HCF of 56, 28 and 84 is given by;

56=2×2×2×728=2×2×784=2×2×3×7

HCFOF56,38and84=2×2×7=28Therefore the required greatest number is 28