Every number is a multiple of itself
A). True
B). False
Answer
557.4k+ views
Hint: First, the product of a number and the other integers are the number that can be called as the multiple of the number. Like the numbers such as even numbers, odd numbers, prime numbers, and composite numbers. All the even numbers have a common factor of $2$ and all the odd numbers have a common factor as $1$.
Complete step-by-step solution:
The numbers may be odd, even, prime or composite in nature, when the number of any kind is multiplied by $1$ gives the number itself. Like $3 \times 1 = 3$
The factors of any number are at least $2$ (one and themself) for the prime numbers and for the composite numbers there are more than two factors like $4$ has three factors $1,2,4$
For all other numbers except prime numbers there are more than two factors.
The number is a multiple of its factor provided that the factors are in the form of integers, the universal fact that any number multiplied by $1$ gets the same integer only. And also, that every number is a multiple of itself too. Even prime numbers like $3$ have two factors: $1,3$ and thus Every number is a multiple of itself. Therefore, the A) Ture is the correct option.
Note: Taking the prime numbers like $2,3,5,7,11$ all of the numbers having the factors as themselves respectively to $2,3,5,7,11$
The composite numbers having the factors to themselves like $4,6,8$ has factors as $4 = 1,2,4$ $6 = 1,2,3,6$ and hence the composite numbers to having the factors as themselves
Once the prime and composite numbers are combined then we don’t even need to check about the odd and even numbers.
Complete step-by-step solution:
The numbers may be odd, even, prime or composite in nature, when the number of any kind is multiplied by $1$ gives the number itself. Like $3 \times 1 = 3$
The factors of any number are at least $2$ (one and themself) for the prime numbers and for the composite numbers there are more than two factors like $4$ has three factors $1,2,4$
For all other numbers except prime numbers there are more than two factors.
The number is a multiple of its factor provided that the factors are in the form of integers, the universal fact that any number multiplied by $1$ gets the same integer only. And also, that every number is a multiple of itself too. Even prime numbers like $3$ have two factors: $1,3$ and thus Every number is a multiple of itself. Therefore, the A) Ture is the correct option.
Note: Taking the prime numbers like $2,3,5,7,11$ all of the numbers having the factors as themselves respectively to $2,3,5,7,11$
The composite numbers having the factors to themselves like $4,6,8$ has factors as $4 = 1,2,4$ $6 = 1,2,3,6$ and hence the composite numbers to having the factors as themselves
Once the prime and composite numbers are combined then we don’t even need to check about the odd and even numbers.
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