Question

10. a and b are two positive integers such that the least prime factor of a is 3 and the least prime factor of bis 5
then find the least prime factor of (a + b)​

Answer 1

Cᴀʟᴄᴜʟᴀᴛɪᴏɴ :

Given that, 

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

Since, least prime factor of a is 3,

• its implies that 'a' is an odd number.

Also, 

• b is a positive integer and 5 is a least prime factor of b, 

Since, least prime factor of b is 5.

• So, b is also an odd number.

and

we know that 

• odd + odd = even 

So,

$\rm :\implies\:a \: + \: b \: is \: even$

$\rm :\implies\: \boxed{ \pink{ \bf \: The \: least \: prime \: factor \: of \:  a + b \: is \:  2. }}$

Answer 2

Answer:

Complete step-by-step answer:

Complete step-by-step answer:In the given question, we are given two positive integers a and b with some conditions on them. So, we are given that the least prime factor of a is 3 and the least factor of b is 5. So, we are required to calculate the least prime factor of sum of the two positive integers given to us.

Complete step-by-step answer:In the given question, we are given two positive integers a and b with some conditions on them. So, we are given that the least prime factor of a is 3 and the least factor of b is 5. So, we are required to calculate the least prime factor of sum of the two positive integers given to us.Hence, the least prime factor of the positive integer a is 3. So, this means that 2 is not a prime factor of a. Hence, we can conclude that the positive integer a is odd.

Complete step-by-step answer:In the given question, we are given two positive integers a and b with some conditions on them. So, we are given that the least prime factor of a is 3 and the least factor of b is 5. So, we are required to calculate the least prime factor of sum of the two positive integers given to us.Hence, the least prime factor of the positive integer a is 3. So, this means that 2 is not a prime factor of a. Hence, we can conclude that the positive integer a is odd.Also, we are given that the least prime factor of the positive integer b is 5. So, this means that 2 is not a prime factor of b. Hence, we can conclude that the positive integer b is also odd.

Complete step-by-step answer:In the given question, we are given two positive integers a and b with some conditions on them. So, we are given that the least prime factor of a is 3 and the least factor of b is 5. So, we are required to calculate the least prime factor of sum of the two positive integers given to us.Hence, the least prime factor of the positive integer a is 3. So, this means that 2 is not a prime factor of a. Hence, we can conclude that the positive integer a is odd.Also, we are given that the least prime factor of the positive integer b is 5. So, this means that 2 is not a prime factor of b. Hence, we can conclude that the positive integer b is also odd.Now, we know that both the positive integers a and b given to us are odd positive integers. So, we have to calculate the least prime factor of (a+b).

Complete step-by-step answer:In the given question, we are given two positive integers a and b with some conditions on them. So, we are given that the least prime factor of a is 3 and the least factor of b is 5. So, we are required to calculate the least prime factor of sum of the two positive integers given to us.Hence, the least prime factor of the positive integer a is 3. So, this means that 2 is not a prime factor of a. Hence, we can conclude that the positive integer a is odd.Also, we are given that the least prime factor of the positive integer b is 5. So, this means that 2 is not a prime factor of b. Hence, we can conclude that the positive integer b is also odd.Now, we know that both the positive integers a and b given to us are odd positive integers. So, we have to calculate the least prime factor of (a+b).We know that the sum of two odd positive integers is even. Hence, we get the sum of the positive odd integers a and b as an even integer. We also know that every even integer is divisible by 2. Moreover, 2 is the least prime number. So, we get the least prime factor of (a+b) as 2.

Complete step-by-step answer:In the given question, we are given two positive integers a and b with some conditions on them. So, we are given that the least prime factor of a is 3 and the least factor of b is 5. So, we are required to calculate the least prime factor of sum of the two positive integers given to us.Hence, the least prime factor of the positive integer a is 3. So, this means that 2 is not a prime factor of a. Hence, we can conclude that the positive integer a is odd.Also, we are given that the least prime factor of the positive integer b is 5. So, this means that 2 is not a prime factor of b. Hence, we can conclude that the positive integer b is also odd.Now, we know that both the positive integers a and b given to us are odd positive integers. So, we have to calculate the least prime factor of (a+b).We know that the sum of two odd positive integers is even. Hence, we get the sum of the positive odd integers a and b as an even integer. We also know that every even integer is divisible by 2. Moreover, 2 is the least prime number. So, we get the least prime factor of (a+b) as 2.So, the correct answer is “2”.

Hope it will help you..