model 3 find hcf of numbers Section-Wise Topic Notes With Detailed Explanation And Example Questions

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The following question based on LCM & HCF topic of quantitative aptitude

Questions : What is the greatest number that will divide 307 and 330 leaving remainders 3 and 7 respectively ?

(a) 23

(b) 16

(c) 19

(d) 17

The correct answers to the above question in:

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).)

The number will be HCF of

307 – 3 = 304 and 330 – 7 = 323.

∴ Required number = 19

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Read more find hcf using formula Based Quantitative Aptitude Questions and Answers

Question : 1

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 : 2

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 : 3

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 : 4

The greatest number that divides 411, 684, 821 and leaves 3, 4 and 5 as remainders, respectively, is

a) 204

b) 146

c) 254

d) 136

Answer: (d)

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 411 – 3 = 408; 684 – 4 = 680 and 821 – 5 = 816

HCF of 408 and 816 = 408

HCF of 408 and 680

∴ Required number = 136

Question : 5

Find the greatest number which will exactly divide 200 and 320.

a) 40

b) 20

c) 10

d) 16

Answer: (a)

Required number = HCF of 200 and 320 = 40

Illustration :

Question : 6

Three sets of English, Mathematics and Science books containing 336, 240, 96 books respectively have to be stacked in such a way that all the books are stored subject-wise and the height of each stack is the same. Total number of stacks will be

a) 48

b) 21

c) 14

d) 22

Answer: (c)

Number of books in each stack

= HCF of 336, 240, 96 = 48

∴ Total number of stacks

=$336/48 + 240/ 48 + 96/48$

=7 + 5 + 2 = 14

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