Question

Which number should be multiplied by $43$ so that it will have $3$ prime factors?

Answer 1

Hint: We first discuss the characteristics of a prime and number. We try to understand the concept with the examples. We also find the factorisation of the number 43. Then we take any two arbitrary unique prime numbers and multiply with 43 to complete the solution.

Complete step by step answer:
Every natural number can be categorised into two parts of prime and composite numbers.We first discuss the characteristics of the prime and composite numbers.The numbers which have only two factors as 1 and that number itself are called prime numbers.

The prime numbers are only divisible by 1 and that number. For example, the numbers 5, 7, 11 are the prime numbers. The factorisation of prime numbers is the multiplication of 1 and that number. 43 can be written as $43=1\times 43$. The number of factorisations for prime numbers is always one but for composite numbers it is at least 2.
Now we multiply 2 and 3 with 43 to get $43\times 2\times 3=258$.
It has 3 unique prime numbers which are 2, 3, 43.

Therefore, the number is 6.

Note: All even numbers are composite numbers except 2. There aren’t enough smaller numbers than 2 to form the factors of 2. Therefore, it’s considered as prime numbers. 1 belongs to neither the prime nor the composite numbers.