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Hint:- Find four smallest prime numbers because we had to find the smallest number.

And the product of the smallest factors will be the smallest number.

First, we will find the first four prime numbers.

As we know that,

Prime numbers are those numbers which had only two factors and that were,

Number itself and one.

So, any number x will be a prime factor if and only if x has only two factors, 1 and x.

As we know that set of some smallest numbers are {1, 2, 3, 4, 5, 6………}

So, out of them the first four prime numbers will be 2, 3, 5 and 7.

Because it is defined that 1 is not a prime number.

And 2, 3, 5 and 7 are only divisible by 1 and the number itself.

So, the product of these four numbers will give us the required smallest number.

Because the product of factors of numbers will give the number itself.

So, required number will be (2) * (3) * (5) * (7) = 210.

Hence, the smallest number having four different prime factors will be 210.

Note:- Whenever we came up with this type of problem then to calculate the

required number efficiently. First, we had to find four smallest prime factors from

the set of all numbers and then we had to multiply these four numbers to get the

smallest number having four different prime factors.

And the product of the smallest factors will be the smallest number.

First, we will find the first four prime numbers.

As we know that,

Prime numbers are those numbers which had only two factors and that were,

Number itself and one.

So, any number x will be a prime factor if and only if x has only two factors, 1 and x.

As we know that set of some smallest numbers are {1, 2, 3, 4, 5, 6………}

So, out of them the first four prime numbers will be 2, 3, 5 and 7.

Because it is defined that 1 is not a prime number.

And 2, 3, 5 and 7 are only divisible by 1 and the number itself.

So, the product of these four numbers will give us the required smallest number.

Because the product of factors of numbers will give the number itself.

So, required number will be (2) * (3) * (5) * (7) = 210.

Hence, the smallest number having four different prime factors will be 210.

Note:- Whenever we came up with this type of problem then to calculate the

required number efficiently. First, we had to find four smallest prime factors from

the set of all numbers and then we had to multiply these four numbers to get the

smallest number having four different prime factors.

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