Question

a and b are two positive integers such that the least prime factor of a is the least parime factor of is 5 them the least prime factor of a+b is
a. 2
b. 3
c. 5
d. 8​

Answer 1

[a] “2” .

$\mathcal{\underbrace{\red{QUESTION:-}}}$

✍️ If a and b are two positive integers such that least prime factor of a is 3 and least prime factor of b is 5 then find the least prime factor of [a+ b] ?

$\mathcal{\underbrace{\red{SOLUTION:-}}}$

GIVEN :-

a is a positive integer and 3 is the least prime factor of a .

Also, b is a positive integer and 5 is the least prime factor of b .

_______________________________

CALCULATION :-

☞ Since least prime factor of a is 3, it

means that a is an odd number .

[ if a is even then 2 is the least prime factor of a .]

☞ Similarly, b is also an odd number .

✍️ Now, it is known that sum of two odd numbers is an even number .

$\rm{\blue{\implies\:a\:+\:b\:=\:3\:+\:5\:=\:8\:}}$

• 8 is an even number .

✍️ Hence, (a + b) will be an even number

✔️So, the least prime factor of (a + b) is 2 .

Answer 2

Answer :–

• Option (a) 2 is the correct.

Correct Question :–

If a and b are two positive integers such that least prime factor of a is 3 and least prime factor of b is 5 then find the least prime factor of a + b is ?

Given :–

• a is a positive integer.
• 3 is the least prime factor of a.
• b is a positive integer.
• 5 is the least prime factor of b.

To Find :–

• Least prime factor of a + b.

Solution :–

a is an odd number because in the given question, 3 is the least prime factor of a.

b is also an odd number because in the given question, 5 is the least prime factor of b.

Here, the least prime factor of a and b is an odd number. So, the least prime factor of a and b is an even number.

We know that,

• odd + odd = even.

• 3 + 5 = 8

• 8 is an even number.

Prime factor of 8 is 2.

So, least prime factor of a + b is 2.

Hence,

The correct option is (a) 2.