Question

Renu purchases two bags of fertilizer of weights 75 kg and 69 kg. Find the maximum value of weight which can measure the weight of the fertilizer exact number of times.

Answer 1

Hint: In this question we are given two quantities and we have to evaluate the maximum value. So, we use the concept of the HCF (Highest Common Factor) to solve this question.

Complete step-by-step answer:

To get a better insight of HCF, we first discuss what is the factor of a number….?
Factors: The numbers that divide a given number completely, i.e., without leaving any remainder, are called factors of that number. For example, 12 is completely divisible by 1, 2, 3, 4, 6, 12.
The largest number that divides two or more numbers is the highest common factor (HCF) for those numbers. For example, consider the numbers \[30\text{ }\left( 2\times 3\times 5 \right),\text{ }18\text{ }\left( 2\times 3\times 3 \right),\text{ }42\text{ }\left( 2\times 3\times 7 \right),\text{ 60 }(2\times 2\times 3\times 5)\]. 3 is the largest number that divides each of these numbers, and hence, is the HCF for these numbers.
HCF is also known as Greatest Common Divisor (GCD).
Now, we have to find the maximum weight in the question.
To do so, we first calculate the HCF of 75 and 69. So, the factors of these numbers can be expressed as
Factors of 75 \[=3\times 5\times 5\]
Factors of 69 $=3\times 23$
The highest common factor of the 75 and 69 is 3.
Hence, the maximum value of weight is 3 kg.

Note: The key concept for solving this question is the knowledge of the highest common factor of two numbers. The highest common factor divides both the number in integral form which is required in our question. This knowledge is useful for solving difficult questions.