Let S be the set of prime numbers greater than or equal to 2 and less ...
For number of zeroes we must count number of 2 and 5 in prime numbers below 100.
We have just 1 such pair of 2 and 5.
Hence we have only 1 zero.
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Let S be the set of prime numbers greater than or equal to 2 and less ...
Basically to get a Zero in the product, an even number should be multiplied with 5.In the entire prime numbers, 2 is the only even number. So only one 0 will be produced in the product of the prime numbers.
Let S be the set of prime numbers greater than or equal to 2 and less ...
Solution:
We know that a number ends with a zero if it has factors of 2 and 5. Thus to calculate the number of trailing zeros in the product of all prime numbers between 2 and 100, we need to count the number of 2s and 5s that are factors of the product.
- Counting the number of 5s: The prime numbers between 2 and 100 that are factors of 5 are 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, and 95. There are 19 of them.
- Counting the number of 2s: Half of the prime numbers between 2 and 100 are even, so they are divisible by 2. There are 49 even prime numbers between 2 and 100, so there are 49 factors of 2.
Since there are only 19 factors of 5, the number of trailing zeros in the product of all prime numbers between 2 and 100 is 1. Therefore, the correct answer is option A.
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