Find the Number of Consecutive Zeros in n = 2³ × 3⁴ × 5⁴ × 7

Video Explanation

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Solution

Question: If

n = 2³ × 3⁴ × 5⁴ × 7

then the number of consecutive zeros in n, where n is a natural number, is:

(a) 2    (b) 3    (c) 4    (d) 7

Important Concept

A zero at the end of a number is produced by a factor of 10.

1 factor of 10 = 2 × 5

So, the number of consecutive zeros depends on the minimum power of 2 or 5 in the prime factorisation.

Step 1: Identify Powers of 2 and 5

Power of 2 = 3

Power of 5 = 4

Step 2: Find the Minimum Power

Minimum of (3, 4) = 3

Final Answer

✔ The number of consecutive zeros in n is 3.

✔ Correct option: (b) 3

Conclusion

Thus, since only 3 pairs of (2 × 5) are possible, the number n ends with 3 consecutive zeros.