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) 8
(b) 5
(c) 4
(d) 6
The correct answers to the above question in:
Answer: (c)
Using Rule 7,
The greatest number N = HCF of (1305 – x ), (4665 – x ) and (6905 – x),
where x is the remainder
= HCF of (4665 – 1305), (6905– 4665) and (6905 – 1305)
= HCF of 3360, 2240 and 5600
∴ N = 1120
Sum of digits = 1 + 1 + 2 + 0 = 4
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Read more find hcf using formula Based Quantitative Aptitude Questions and Answers
Question : 1
There are 24 peaches, 36 apricots and 60 bananas and they have to be arranged in several rows in such a way that every row contains the same number of fruits of only one type. What is the minimum number of rows required for this to happen ?
a) 6
b) 9
c) 12
d) 10
Answer »Answer: (d)
Minimum number of rows = Maximum number of fruits in each row
∴ HCF of 24, 36 and 60 = 12
∴ Minimum number of rows
= $24/12 + 36/12 + 60/12$
= 2 + 3 + 5 = 10
Question : 2
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 »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 : 3
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 »Answer: (a)
First of all we find HCF of 391 and 323.
∴ Number of classes = 17
Question : 4
84 Maths books, 90 Physics books and 120 Chemistry books have to be stacked topicwise. How many books will be there in each stack so that each stack will have the same height too ?
a) 21
b) 18
c) 12
d) 6
Answer »Answer: (d)
As the height of each stack is same,
the required number of books in each stack
= HCF of 84, 90 and 120
84 = 2 × 2 × 3 × 7
90 = 2 × 3 × 3 × 5
120 = 2 × 2 × 2 × 3 × 5
∴ HCF = 2 × 3 = 6
Question : 5
H.C.F of $2/3,4/5$and $6/7$ is
a) $24/105$
b) $2/105$
c) $48/105$
d) $1/105$
Answer »Answer: (b)
Using Rule 3,
(H.C.F. of fractions =$\text"H.C.F of numerators"/ \text"L.C.M.of denominators"$)
HCF of $2/3,4/5$and $6/7$
= $\text"H.C.F of 2,4 and 6"/ \text"L.C.M.of 3,5 and 7"$
= $2/105$
Question : 6
The product of two 2–digit numbers is 2160 and their H.C.F. is 12. The numbers are
a) (60, 72)
b) (72, 30)
c) (12, 60)
d) (36, 60)
Answer »Answer: (d)
HCF of numbers = 12
Let the numbers be 12x and 12y
where x and y are co–prime.
According to the question,
12x × 12y = 2160
⇒ xy = $2160/{ 12×12}$ = 15
= 3 × 5 or 1 × 15
∴ Required numbers
= 12 × 3 = 36 and 12 × 5 = 60
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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