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

Question : 21 [SSC CAPFs SI, 2014]

Three tankers contain 403 litres, 434 litres, 465 litres of diesel respectively. Then the maximum capacity of a container that can measure the diesel of the three containers exact number of times is

a) 84 litres

b) 62 litres

c) 31 litres

d) 41 litres

Answer: (c)

Greatest capacity of measuring vessel

= HCF of 403 litres, 434 litres and 465 litres

= 31 litres

Illustration :

HCF of 403 and 434

Question : 22

A milkman has 75 litres milk in one can and 45 litres in another. The maximum capacity of container which can measure milk of either container exact number of times is :

a) 25 litres

b) 5 litres

c) 1 litre

d) 15 litres

Answer: (d)

Required maximum capacity of container

= HCF of 75 l and 45 l

Now, 75 = 5 × 5 × 3

45 = 5 × 3 × 3

∴ HCF = 15 litres

Question : 23 [SSC FCI 2012]

What is the greatest number which will divide 110 and 128 leaving a remainder 2 in each case ?

a) 38

b) 18

c) 8

d) 28

Answer: (b)

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 (110 – 2) and (128 – 2)

= HCF of 108 and 126 = 18

Question : 24 [SSC CHSL 2014]

The greatest number that will divide 729 and 901 leaving remainders 9 and 5 respectively, is

a) 20

b) 16

c) 15

d) 19

Answer: (b)

Using Rule 7,

Required number

= HCF of (729 – 9)

= 720 and (901 – 5)

= 896

H.C.F = 16

Question : 25

The maximum number of students among whom 1001 pens and 910 pencils can be distributed in such a way that each student gets same number of pens and same number of pencils, is :

a) 1911

b) 910

c) 91

d) 1001

Answer: (c)

Maximum number of students

= The greatest common divisor

= HCF of 1001 and 910 = 91

IMPORTANT quantitative aptitude EXERCISES

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