model 3 find hcf of numbers Practice Questions Answers Test with Solutions & More Shortcuts

Question : 6 [SSC Constable 2012]

A milk vendor has 21 litres of cow milk, 42 litres of toned milk and 63 litres of double toned milk. If he wants to pack them in cans so that each can contains same litres of milk and does not want to mix any two kinds of milk in a can, then the least number of cans required is

a) 12

b) 6

c) 3

d) 9

Answer: (b)

Maximum quantity in each can

= HCF of 21, 42 and 63 litres

= 21 litres

Required least number of cans

= $21/21 + 42/ 21 + 63/21$

= 1 + 2 + 3 = 6

Question : 7

In a school, 391 boys and 323 girls have been divided into the largest possible equal classes, so that each class of boys numbers the same as each class of girls. What is the number of classes ?

a) 17

b) 19

c) 23

d) 44

Answer: (a)

First of all we find HCF of 391 and 323.

∴ Number of classes = 17

Question : 8 [SSC SO 2006]

The greatest number, by which 1657 and 2037 are divided to give remainders 6 and 5 respectively, is

a) 305

b) 133

c) 127

d) 235

Answer: (c)

Using Rule 7,

(The largest number which when divide the numbers a, b and c give remainders as p, q, r respectively is given by H.C.F. of (a – p), (b – q) and (c – r).)

We have to find HCF of

(1657 – 6 = 1651) and (2037 – 5 = 2032)

1651 = 13 × 127

2032 = 16 × 127

∴ HCF = 127

So, required number will be 127.

Question : 9

What is the least number of square tiles required to pave the floor of a room 15 m 17 cm long and 9 m 2 cm broad?

a) 814

b) 841

c) 840

d) 820

Answer: (a)

Length of the floor

= 15 m 17 cm = 1517 cm

Breadth of the floor

= 9m 2 cm = 902 cm.

Area of the floor

= 1517 × 902 $cm^2$

The number of square tiles will be least, when the size of each tile is maximum.

∴ Size of each tile = HCF of 1517 and 902 = 41

∴ Required number of tiles

=${1517× 902}/{41× 41}$ = 814

Question : 10 [SSC CAPFs SI, 2015]

The greatest number by which 2300 and 3500 are divided leaving the remainders of 32 and 56 respectively, is

a) 84

b) 168

c) 136

d) 42

Answer: (a)

Using Rule 7,

(The largest number which when divide the numbers a, b and c give remainders as p, q, r respectively is given by H.C.F. of (a – p), (b – q) and (c – r). )

Required number

= HCF of 2300 – 32

= 2268 and 3500 – 56 = 3444

∴ HCF = 84

IMPORTANT quantitative aptitude EXERCISES

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