Real numbers
Grade Class 10
Question:
<p>If 3 is the least prime factor of number 'a' and 7 is the least prime factor of number 'b', then the least prime factor of a + b, is</p>
<p style="display:inline">10</p>
<p style="display:inline">3</p>
<p style="display:inline">5</p>
<p style="display:inline">2</p>
Step-by-Step Solution
Key Concept: If the least prime factor of a number is greater than 2, the number must be odd, and the sum of two odd numbers is always an even number whose least prime factor is 2.
<p>Since 7 + 3 = 10<br />
The least prime factor of a + b has to be 2; unless a + b is a prime number greater than 2.<br />
Suppose a + b is a prime number greater than 2. Then a + b must be an odd number<br />
and one of 'a' or 'b' must be an even number.<br />
Suppose that 'a' is even. Then the least prime factor of a is 2; which is not 3 or 7. So 'a' can not be an even number nor can b be an even number. Hence a + b can not be a prime number greater than 2 if the least prime factor of a is 3 and b is 7.<br />
Thus the answer is 2.</p>
Correct Answer: D