Answer

Verified

430.5k+ views

**Hint:**We try to find out the concept of multiplier. we express the given number termed as a multiplication form of two other positive whole numbers. We also check whether it is directly divisible by 3 or 5 using the division formulas of 3 and 5.

**Complete step-by-step solution:**The concept of a number is a multiple of another number comes from the concept of divisibility or expression of the first number being termed as a multiplication form of two other positive whole numbers different from the given first number.

So, we need to check the divisibility of 60 by 3 and 5.

For the divisibility of 3, we know that if the sum of the digits in a number is divisible by 3 then the number itself is divisible by 3.

For example, we take a number (abc) where a, b, c are the digits in that number in the hundredth, tenth, unit places. So, we find $a+b+c$. If the sum is divisible by 3 then (abc) is divisible by 3. Take 4747. We add up the digits and get $4+7+4+7=22$ which is not divisible by 3. So, 4737 is not divisible by 3 where $\dfrac{4747}{3}=1582.3 $.

For the divisibility of 5, we know that if the last digit i.e. the unit place digit is 0 or 5 then the number itself is divisible by 5.

For example, we take a number (abc) where a, b, c are the digits in that number in the hundredth, tenth, unit places. So, we find c. If c is 0 or 5 then (abc) is divisible by 5. Take 4735. We have 5 in unit place, so it’s divisible by 5. So, 4735 is divisible by 5 where $\dfrac{4735}{5}=947$.

Now we talk about 60. The sum of the digits is $6+0=6$ which is divisible by 3. So, 60 is divisible by 3.

60 has 0 in its unit place. So, 60 is also divisible by 5.

Now we express 60 as a multiplication of two positive whole numbers.

So, $60=3\times 20$. In this factorization of 60, we have two positive whole numbers and 3 and 20 which means 60 is a multiple of 3 when it’s multiplied by 20.

Again $60=5\times 12$. In this factorization of 60, we have two positive whole numbers and 5 and 12 which means 60 is a multiple of 5 when it’s multiplied by 12.

**So, the given statement is true. The correct option is (A).**

**Note:**We need to remember the theorems for the divisibility. If we can’t then there will be no way to find out other than doing long division. Using the theorem saves a lot of time. The multiplication form is also very important to establish the statement as true.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Trending doubts

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference Between Plant Cell and Animal Cell

Which are the Top 10 Largest Countries of the World?

Write a letter to the principal requesting him to grant class 10 english CBSE

10 examples of evaporation in daily life with explanations

Give 10 examples for herbs , shrubs , climbers , creepers

Change the following sentences into negative and interrogative class 10 english CBSE