Question:
Find the number of zeros at the end of the product :
5 × 10 × 15 × 20 × 25 × ……………………..× 500
Find the number of zeros at the end of the product :
5 × 10 × 15 × 20 × 25 × ……………………..× 500
5 × 10 × 15 × 20 × 25 × ……………………..× 500
Updated On: Sep 10, 2024
- 85
- 92
- 87
- 97
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The Correct Option is D
Solution and Explanation
5 × 10 × 15 × 20 × 25 × …………………….. × 500
The above expression can be written as :
5100 × 100!
For finding the number of zeros, we need to calculate the integral greatest power (IGP) of 2 and 5. One with the lesser power will decide the number of zeros.
In 100!, IGP of 5: 20 + 4 = 24
Since, 100 powers of 5 are already there, so overall integral power of 5 is 124.
In 100!, IGP of 2 : 50 + 25 + 12 + 6 + 3 + 1 = 97
Since the IGP of 2 is less than IGP of 5, the number of zeros at the end of the product will be 97.
So, the correct option is (D) : 97.
The above expression can be written as :
5100 × 100!
For finding the number of zeros, we need to calculate the integral greatest power (IGP) of 2 and 5. One with the lesser power will decide the number of zeros.
In 100!, IGP of 5: 20 + 4 = 24
Since, 100 powers of 5 are already there, so overall integral power of 5 is 124.
In 100!, IGP of 2 : 50 + 25 + 12 + 6 + 3 + 1 = 97
Since the IGP of 2 is less than IGP of 5, the number of zeros at the end of the product will be 97.
So, the correct option is (D) : 97.
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