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Number Theory Level 2

Find the number of trailing zeroes in the product of the first 2007 (positive) prime numbers.


The answer is 1.

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Krishna Ar by Krishna Ar , 21, India

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7 solutions

For a number to end with zero, it must be a multiple of both 2 and 5. If we closely look at the list of prime numbers, 2 and 5 will occur only once and their multiples will not. Since there is only one 2*5 pair, there will be one one zero. Answer is therefore 1.

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to give end digits as zeros product should be done between the numbers containing as end digits As(2 &4),(4&5) ,(6 &5), (8,5),(0 & any num) but no prime num is end digit with 4,6,8,0. Therefore the prime num multiplication which produce ended zero is b/w ( 2 &5 only).

MaNmohan Reddy - 7 years, 1 month ago

yeah..I did the same...damn easy !!

Max B - 7 years, 1 month ago

yes that is write no more multiples of five or two's that is why it should only have one zero or the lowest prime numbers taht is even or multiples of two is two itself

Melchor Sioting - 7 years, 1 month ago

multiple of 2 and 5 is 10

Dileep Kumar - 7 years, 1 month ago
Vishal S
Jan 20, 2015

Since the product of prime numbers; 2 & 5 is 10 and there is no primes which give rise zeroes greater than 1 zeroes.

Therefore the number of trailing zeroes in the product of 1st 2007 prime numbers is 1

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S Sen
Jun 18, 2014

To have a trailing zero, we need a '10' and to have a 10 we need a 2 & 5. Since we are considering the product of prime nos only, 2 and 5 will occur in the product only once..... so only 1 trailing zero :-)

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Sivasankar P
May 7, 2014

There exists only one Zero since only one even prime number... :p

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Only product of 2 and 5 yields a prime number all other prime product not ends with a zero :-)

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Suman Singh
Apr 25, 2014

A Multiplication of two Number, result ended with Zero if the unit place of Numbers have (0, 2, 4, 5, 6, 8) But any one of these Numbers at unit place of two digit or more then two, Number then it will not be prime. so, these six number contains four (0, 4, 6, 8) are even and remaining two (2, 5) are prime Number. The multiplication of these two 2 and 5 results a single Zero.

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Kevin Bourrillion
Apr 24, 2014

I missed the word "prime" so I interpreted it as the number of trailing zeroes in 2007 factorial. The answer to that problem is kinda neat; try it.

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https://brilliant.org/community-problem/again-2007/?group=Yu37znGmjpiB&just_created=true Do try this, this is the problem to which you perhaps answered.

Krishna Ar - 7 years, 1 month ago

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nice!

Kevin Bourrillion - 7 years, 1 month ago

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