Find the Exponent of 2 in the Prime Factorisation of 144

Video Explanation

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Solution

Question: The exponent of 2 in the prime factorisation of 144 is:

(a) 4    (b) 5    (c) 6    (d) 3

Step 1: Prime Factorisation of 144

144 = 12 × 12

12 = 2 × 2 × 3

∴ 144 = (2 × 2 × 3) × (2 × 2 × 3)

144 = 2⁴ × 3²

Step 2: Identify the Exponent of 2

In the prime factorisation 2⁴ × 3², the exponent of 2 is 4.

Final Answer

✔ Correct option: (a) 4

Conclusion

Thus, the exponent of 2 in the prime factorisation of 144 is 4.