a and b are Two Positive Integers such that the Least Prime Factor of a is 3 and and that of b is 5. Find the Least Prime Factor of (a+b).

By BYJU'S Exam Prep

Updated on: September 25th, 2023

The least prime factor of (a+b) is 2 where a and b are two positive integers with the least prime factor of ‘a’ being 3 and the least prime factor of ‘b’ being 5. We know that the sum of two odd numbers is an even number. Hence, the least prime factor of (a + b) should be even.

Since 3 is the least prime factor of the positive integer ‘a;. So, 2 is not a prime factor of ‘a’. Hence, the positive integer ‘a’ must be odd.

Also, the least prime factor of the positive integer ‘b’ is 5. Hence, 2 is not a prime factor of ‘b’. Therefore, we can deduce that the positive integer ‘b’ is also odd.

Additionally, we are aware that all even numbers can be divided by 2 and 2 is the smallest prime number. Therefore, 2 is the smallest prime factor of (a+b).

Table of content

1. Least Prime Factor of (a+b) for Value of ‘a’ being 3 and ‘b’ being 5
2. a and b are Two Positive Integers such that the Least Prime Factor of a is 3 and and that of b is 5. Find the Least Prime Factor of (a+b).

Least Prime Factor of (a+b) for Value of ‘a’ being 3 and ‘b’ being 5

As discussed above, 2 is the least prime factor of (a+b) for the value of ‘a’ being 3 and ‘b’ being 5. Now let us understand what a Prime Factor is.

A natural number other than 1 whose only factors are 1 and itself is called a prime factor. Actually, 2, 3, 5, 7, 11, and so forth are the first few prime numbers. We can easily determine the prime factors of any number by doing its prime factorization. The process of writing all numbers as the product of primes is known as prime factorization.

Example – Prime factors of 12 = 2 × 2 × 3

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