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if least prime factor of a is 3 and the least prime factor of b is 5 then what is the least prime factor of (a+b)

Posted by Sameer Ali 6 years, 10 months ago

CBSE > Class 10 > Mathematics

2 answers

Ram Kushwah 6 years, 10 months ago

Least prime factor of a is 3 then 2 is not factor

as 3< 2

so a is odd number

Least prime factor of a is 5 then 2 is not factor

as 5< 2

so b is odd number

so a+b= odd number +odd number = even number

so a+b=2q ( q is any positive integer

hence least prime factor of a+b is 2

Gaurav Seth 6 years, 10 months ago

Given that, 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.

Since least prime factor of a is 3, it means that a is an odd number.

So, 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.

Hence, a + b will be an even number.

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

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