Question

Suppose that you have four
containers of 42, 210, 98 and 294
liters and you have to use a bucket of
the largest volume with which all the
bucket's water could be measured
exactly. Find the number of buckets
required to measure the volume of all
the containers together.​

Answer 1

Answer:

(1) 14 litres (2) 46

Step-by-step explanation:

hcf of 42,210,98,294 is 14 . next 42/14+210/14+98/14+294/14=46

Answer 2

The volume of all containers measured exactly will be 14litres.

The number of buckets required⇒46.

Step-by-step explanation:

Given:

four containers of 42, 210, 98, and 294 liters

To find:

The largest volume with which all the bucket's water could be measured exactly

The number of buckets required to measure the volume of all the containers together.​

Solution:

• From the given data, Four containers of 42, 210, 98, and 294 liters
• We have to use a bucket of the largest volume with which all the bucket's water could be measured exactly which means the highest common factor(HCF).

        ⇒Multipliers of 42⇒ 2×3×7

        ⇒Factors of 210⇒ 2×3×5×7

        ⇒Factors of 98⇒ 2×7×7

        ⇒Factors of 294⇒ 2×3×7×7

        ⇒HCF of 42,210,98,294 is 2×7=14

        ⇒HCF=14.

The largest volume with which all the bucket's water could be measured exactly is 14litres.

The number of buckets required= $\frac{42}{14}$+$\frac{210}{14}$+$\frac{98}{14}$+$\frac{294}{14}$

                                                      ⇒3+15+7+21

The number of buckets required⇒46.

Hence,

The volume of all containers measured exactly will be 14litres.

The number of buckets required⇒46.