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) 46 and 75
(b) 9 and 380
(c) 15 and 228
(d) 45 and 76
The correct answers to the above question in:
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
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Read more find hcf using formula Based Quantitative Aptitude Questions and Answers
Question : 1
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 : 2
Find the greatest number that will divide 390, 495 and 300 without leaving a remainder.
a) 35
b) 15
c) 5
d) 25
Answer »Answer: (b)
Required number = HCF of 390, 495 and 300 = 15
Illustration :
HCF of 15 and 300 = 15
Question : 3
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 : 4
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
Question : 5
Which greatest number will divide 3026 and 5053 leaving remainders 11 and 13 respectively?
a) 60
b) 30
c) 18
d) 45
Answer »Answer: (d)
Using Rule 7,
3026 –11 = 3015 and 5053 –13 = 5040
Required number = HCF of 3015 and 5040
∴ Required number = 45
Question : 6
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 »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
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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