Question

What is the sum of the two smallest natural numbers each of the two having exactly seven fac

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

The sum of the two smallest natural numbers having exactly seven factors is 793.

Step-by-step explanation:

• The number of prime factors of a number can be found from the prime factorization of a number.
• If the prime factorization of a number is given by  

        $p^x\times q^y\times...$

       then the product of the exponents increased by one, i.e.,

       $(x+1)\times (y+1)\times...$

       equals the number of prime factors of a number.

Given the two natural numbers have exactly seven factors.

Thus, to get the product 7,

consider $p^x$, add 1 to $x$ that must be 7, i.e., $6+1 = 7$.

So, the number is $p^{2}$ .

The two smallest primes are 2 and 3.

Therefore, the two smallest numbers having exactly seven factors are

$2^6 = 64$ and $3^6 = 729$.

Sum of the two numbers is

$64+729=793$

Hence, the sum of the two smallest natural numbers having exactly seven factors is 793.

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