NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 1: Number System - Multiple Choice Questions
Question 32

Question.  32

The sum of the prime factors of 1729 is

(A)

13

(B)

19

(C)

32

(D)

39

Detailed Answer with Explanation:

Step 1: Try dividing 1729 by small primes.

Not by 2, because 1729 is odd.

Not by 3, because \(1+7+2+9 = 19\) (not a multiple of 3).

Not by 5, because the last digit is 9 (not 0 or 5).

Step 2: Try 7.

\(1729 \div 7 = 247\)

So, \(1729 = 7 \times 247\).

Step 3: Factor 247.

Not by 2, 3, or 5 (same checks as before).

Check 7: \(7 \times 35 = 245\), so not exact.

Check 11: \(11 \times 22 = 242\), so not exact.

Check 13: \(247 \div 13 = 19\)

So, \(247 = 13 \times 19\).

Step 4: Confirm primes.

13 and 19 are both prime numbers.

Step 5: Write the prime factorization.

\(1729 = 7 \times 13 \times 19\)

Step 6: Add the prime factors.

\(7 + 13 + 19 = 39\)

Answer: 39 (Option D).

NCERT Exemplar Solutions Class 6 – Mathematics – Unit 1: Number System – Multiple Choice Questions | Detailed Answers