Least Prime Factor of a + b When Least Prime Factors of a and b Are Given

Video Explanation

Watch the video below for a clear explanation:

Solution

Question: 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:

(a) 2    (b) 3    (c) 5    (d) 10

Step 1: Understand the Given Information

If 3 is the least prime factor of a, then a is divisible by 3 and a is an odd number.

If 7 is the least prime factor of b, then b is divisible by 7 and b is also an odd number.

Step 2: Determine the Nature of a + b

Odd number + Odd number = Even number

So, a + b is an even number.

Step 3: Find the Least Prime Factor

The least prime factor of any even number (greater than 2) is 2.

Final Answer

✔ The least prime factor of a + b is 2.

✔ Correct option: (a) 2

Conclusion

Since both a and b are odd numbers, their sum is even, and therefore the least prime factor of a + b is 2.