Find the Sum of the Exponents of the Prime Factors of 196

Video Explanation

Watch the video below for a clear explanation:

Solution

Question: The sum of the exponents of the prime factors in the prime factorisation of 196 is:

(a) 1    (b) 2    (c) 4    (d) 6

Step 1: Prime Factorisation of 196

196 = 14 × 14

14 = 2 × 7

∴ 196 = (2 × 7) × (2 × 7)

196 = 2² × 7²

Step 2: Find the Sum of the Exponents

Exponent of 2 = 2

Exponent of 7 = 2

Sum of the exponents = 2 + 2 = 4

Final Answer

✔ Correct option: (c) 4

Conclusion

Thus, the sum of the exponents of the prime factors in the prime factorisation of 196 is 4.