Question

if 3 is a least factor of number and 7 is the least factor of b then the least prime factor of a+b is​

Answer 1

It is given that 3 is the least prime factor of number a and 7 is the least prime factor of number b. Therefore, a should be greater than or equal to 3 and b should be greater than or equal to 7.

$\bold{That \: is \: a≥3 {}^{1} \: and \: b≥ {7}^{1} }$

Now, consider the case a=3 and b=7

Then, a+b=3+7=10

Then, 2 is the least prime factor of a+b.

$\small \bold{Let \: us \: consider \: the \: case \: a=3^2=9 \: and \: b=7^2=49}$

So, it is clear that a+b=58 which is an even number.

Similarly, for the value of n,

$\bold{ {a}^{n} + {b}^{n} \: is \: divisible \: by  \: 2.}$

Hence, the least prime factor of a+b is 2