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What is the greatest number that will divide 172, 205 and 304 so as to leave the same remainder in each case?

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posted Sep 10 by anonymous

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3 Solutions

+1 vote

The answer is 33

Lets put them into equations
172 = D*q1 + r1;
205 = D*q2 + r2;
304 = D*q3 + r3;

and r1=r2=r3=r

so.
D*(q2-q1)= 33
D*(q3-q2)= 99
D*(q3-q1)= 132

For the greatest value of D take the HCF of 33, 99 and 132 which is 33.

solution Sep 10 by Salil Agrawal
0 votes

shortcut

step1 let assume a=172
b=205
c=304
step2 take difference
(b-a)=33
(c-b)=99
(c-a)=132
now take a HCF of these numbers(33,99,132)
HCF=33(ans)

solution Sep 11 by Thanganila Muthumurugan
0 votes

33 is the answer
Explanation:
The greatest number that will divide 172,205 and 304 leaving the same remainder in each
case is HCF ((205-172), (304-205), (304-172))
= HCF of 33, 99, and 132
33=31x11
99=3 x 3 x 11
132=3 x 2 x 2 x11
Required number =3 x 11=33

solution Sep 12 by Mogadala Ramana



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