State whether the following statement is True or False:
Statement: 60 is a multiple of 3 and 5.

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True

False

answer is A.

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Detailed Solution

The concept of a number is a multiple of another number comes from the concept of divisibility
Here, we are required to check the divisibility of 60 by 3 and 5.
We know the rule for divisibility of 3, that if the sum of the digits in a number is divisible by 3 then the number itself is divisible by 3.
Now we 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

\frac{4747}{3}

=1582.3.
We know that 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.
Now, we take 4735. We have 5 in the unit place, so it’s divisible by 5. So, 4735 is divisible by 5 where

\frac{4735}{3}

= 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 × 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 × 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 (1).

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