model 3 find hcf of numbers Section-Wise Topic Notes With Detailed Explanation And Example Questions
MOST IMPORTANT quantitative aptitude - 5 EXERCISES
The following question based on LCM & HCF topic of quantitative aptitude
(a) 35
(b) 15
(c) 5
(d) 25
The correct answers to the above question in:
Answer: (b)
Required number = HCF of 390, 495 and 300 = 15
Illustration :
HCF of 15 and 300 = 15
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Read more find hcf using formula Based Quantitative Aptitude Questions and Answers
Question : 1
The greatest number, which when divide 989 and 1327 leave remainders 5 and 7 respectively, is :
a) 32
b) 16
c) 8
d) 24
Answer »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 (989 – 5) and (1327 – 7)
= HCF of 984 and 1320 = 24
∴ HCF = 24
Question : 2
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 »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
Question : 3
Find the greatest number which will exactly divide 200 and 320.
a) 40
b) 20
c) 10
d) 16
Answer »Answer: (a)
Required number = HCF of 200 and 320 = 40
Illustration :
Question : 4
The largest number, which divides 25, 73 and 97 to leave the same remainder in each case, is
a) 6
b) 23
c) 24
d) 21
Answer »Answer: (c)
Using Rule 7,
Let x be the remainder.
Then, (25 – x ), (73 – x ), and (97 – x )
Will be exactly divisible by the required number.
∴ Required number
= HCF of (73 –x ) – (25 –x ), (97 –x ) – (73 –x ) and (97 –x ) – (25 –x )
= HCF of (73 –25), (97 –73), and (97 –25)
= HCF of 48, 24 and 72 = 24
Question : 5
A farmer has 945 cows and 2475 sheep. He farms them into flocks, keeping cows and sheep separate and having the same number of animals in each flock. If these flocks are as large as possible, then the maximum number of animals in each flock and total number of flocks required for the purpose are respectively
a) 46 and 75
b) 9 and 380
c) 15 and 228
d) 45 and 76
Answer »Answer: (d)
First of all we find the HCF of 945 and 2475. HCF = 45
Illustration :
∴ Maximum number of animals in each flock = 45
Required total number of flocks = $945/45 + 2475/45$
= 21 + 55 = 76
Question : 6
Two pipes of length 1.5 m and 1.2 m are to be cut into equal pieces without leaving any extra length of pipes. The greatest length of the pipe pieces of same size which can be cut from these two lengths will be
a) 0.41 metre
b) 0.4 metre
c) 0.13 metre
d) 0.3 metre
Answer »Answer: (d)
Maximum length of each piece
= HCF of 1.5 metre and 1.2 metre
= 0.3 metre
Illustration :
∴ HCF of 1.5 and 1.2 metre = 0.3 metre
LCM & HCF Shortcuts and Techniques with Examples
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model 1 Basic formula of LCM & HCF
Defination & Shortcuts … -
model 2 find lcm of numbers
Defination & Shortcuts … -
model 3 find hcf of numbers
Defination & Shortcuts … -
model 4 addition, subtraction, multiplication and division with lcm & hcf
Defination & Shortcuts … -
model 5 lcm & hcf vs ratios
Defination & Shortcuts …
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