Applications of HCF

Q.

Three tankers contain $403$ liters, $434$ liters and $465$ liters of diesel respectively. Find the capacity of a container that can measure the diesel of three containers exact number of times.

Q.

Two tankers contain 200 litres and 440 litres of petrol respectively.
The maximum capacity of a container which can measure the petrol of either tank in the exact number of times is ____ litres.

1. 20
2. 30
3. 40
4. 50

Q. A car park has 12 rows of parking lots. An equal number of cars can be parked in each parking lot. If there are 168 cars, how many cars can be parked in each row?

1. 16
2. 18
3. 12
4. 14

Q. The product of two numbers is 228. If their HCF is 12, then what will be their LCM?

1. 20

2. 1

3. 19

4. 0

Q. Which of the following explains the relation between any two given numbers and their HCF and LCM?

1. Product of the two numbers = Product of their HCF and LCM
2. First number $\times$ HCF = Second number $\times$ LCM
3. Difference between the two numbers = Difference between their HCF and LCM
4. Sum of the two numbers = Sum of their HCF and LCM

Q. A 14 cm long stick is to be divided into smaller pieces of equal length. If minimum number of pieces are 2, then the maximum length of each smaller pieces will be ________

1. 14 cm
2. 7 cm
3. 6 cm
4. 2 cm

Q. The highest step size one can take to reach both steps 24 and 16 is?

1. 8

Q.

Find the HCF using the common factor method .

$36,$$30$ and $120$

Q.

What is greatest common factor?

Q. Janet has 28 green beads, 84 red beads and 56 orange beads. She wants to pack them such that each bag contains the same number of beads of each color. What is the greatest number of bags she can pack?

1. 14
2. 6
3. 7
4. 28

Q. Aman has three ropes of length 9 m, 12 m and 15 m. He wants to split them further into pieces of equal and largest possible length. What should be the length of each piece?

1. 180 m
2. 9 m
3. 3 m
4. 1 m

Q. The highest step size one can take to reach both steps 24 and 16 is ____.

1. 6
2. 8
3. 4
4. 2

Q.

The HCF of 75 and 90 is 15. What is their LCM?

1. 150
2. 180
3. 300
4. 450

Q.

The product of two numbers is 600. If their HCF is 5, then what is their LCM?

1. 120

2. 60

3. 40

4. 50

Q. Catherine arranges 624 books in 3 racks. Each rack has 4 shelves. How many books are there in each shelf?

1. 56
2. 50
3. 52
4. 54

Q.

Three tankers contain $434$ litres, $465$ lites and $403$ lites of fuel respectively. What should be the maximum capacity of a container that can measure the fuel of the three containers exact number of times.

Q. 72 books were arranged equally on 8 shelves. How many books are there on each shelf?

1. 72

2. 8

3. 18

4. 9

Q. Two tanks A and B contain 85 litres and 68 litres of oil respectively. Find the maximum capacity of a container which can exactly measure the oil in both the tanks.

1. 15 litres
2. 17 litres
3. 19 litres
4. 13 litres

Q. There are $10$ red straws and $8$ blue straws. The straws are divided equally among $6$ students. How many straws does each student get?

Q. Ananya has 38 sharpners, 152 pencils and 114 erasers. How many maximum number of each one pencil box contains if she wants to pack same number of each in a number of pencil boxes.

1. 2 sharpner,
   3 pencils,
   3 erasers
2. 4 sharpner,
   3 pencils,
   1 erasers
3. 1 sharpner,
   4 pencils,
   3 erasers
4. 1 sharpner,
   3 pencils,
   4 erasers