Word Problems on H.C.F.

Let us consider some of the word problems on H.C.F. (highest common factor).

1. Two wires are 12 m and 16 m long. The wires are to be cut into pieces of equal length. Find the maximum length of each piece.

To find the maximum length, we find the H.C.F. of 12 and 16.

H.C.F. = 4 

The maximum length of each piece is 4 m. 

2. Find the greatest number which is less by 2 to divide 24, 28 and 64 exactly.

First we find the H.C.F. of 24, 28 and 64.

H.C.F. = 4

The required number is 4 - 2 = 2.

(We see that 2 is less than 4 by 2.)

3. Find the greatest number that divides 90 and 126 exactly.

Solution:

The greatest number that divides both 90 and 126 exactly is their HCF.

We can find HCF by long division method.

HCF of 90 and 126 is 18.

4. Rachel has 24 red candies and Maya has 18 green candies. They want to arrange the candies in such a way that each row contains equal number of candies and also each row should have only red candies or green candies. What is the greatest number of candies that can be arranged in each row?

Solution:

In order to find the greatest number of candies that can be arranged in equal rows, we find the HCF of two numbers.

Factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24.

Factors of 18 are 1, 2, 3, 6, 9 and 18.

The highest common factor is 6.

So, the greatest number of candies that can be arranged in each row is 6.

5. Two drums contain 415 litres and 385 litres of kerosene oil respectively. Find the maximum capacity of a big container which can measure the kerosene oil of both the drums when used an exact number of times.

Solution:

The maximum capacity of a big container will be the HCF of 415 and 385.

The HCF of 415 and 385 is 5.

Hence, the maximum capacity of a big container is 5 litres.

Worksheet on Word Problems on HCF:

1. Find the largest number that divides 348 and 626 leaving remainders 3 and 5 respectively.

2. Find the largest number that divides 283, 390 and 532 leaving remainders 3, 5 and 7 respectively.

3. A rectangular wall of size 11 m 20 cm and 9 m 60 cm is paved with square marble st of the same size. Find the least number of marble stones required.

[Hint: HCF of 1120 and 960 = 160 (side of one stone) 

Least no. of stones = \(\frac{1120 × 960}{160 × 160}\) = 42]

4. Three water tankers contain 1470 ℓ, 2688 ℓ and 4032 ℓ of water respectively. Find maximum capacity of a container which can measure the water of each container in exact number of times.

5. A shopkeeper has three different qualities of sugar filled in containers of 234 kg, 520 kg and 975 kg. If he wants to pack them in exact number of bags, what should be the capacity of a bag?

Answers:

1. 69

2. 35

3. 42 stones

4. 42 ℓ

5. 13 kg

4th Grade Math Activities

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