math kangaroo contest question
in Word Problem Answers by

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

2 Answers

??????????? "natural numbers" ?????????

em thangs be INTEGER

produkt av 1*2*3*... is kalled the FAKTORIAL

50!=30,414,093,201,713,378... 65 digits

it hav 12 zeroes at rite end
by

To calculate the number of zeroes all we need to do is to consider the different numbers that generate at least one zero at the end of their product. 10=2*5 is the main generator, so (2*5)^n generates n zeroes at the end of the product. So we have between 1 and 50: 2, 4, 8, 16 and 32; and 5 and 25; but we also have 10, 20, 30, 40 and 50, as well as 15, 35 and 45 which generate a zero with even numbers: 6, 12, 14, 18, 22, 24, 26, 28, 34, 36, 38, 42, 44, 46, 48. We can't use any natural number more than once, so we need to pair up just three even numbers with the three ending in 5. No other numbers between 1 and 50 will generate any more zeroes.

So let's collect the generators.

2*5, 4*25, 8*15, 16*35, 32*45 generate 6 zeroes between them.

10*20*30*40*50=12000000 generate a further 6 because 20*50=1000, giving an extra zero.

Therefore, there must be 12 zeroes at the end of 50! (shorthand for 1*2*3*4*...*50).

 

by Top Rated User (1.2m points)

Related questions

1 answer
asked Apr 7, 2014 in Other Math Topics by AAYUSH Level 1 User (120 points) | 1.2k views
1 answer
asked Aug 10, 2014 in Other Math Topics by anonymous | 2.7k views
1 answer
1 answer
asked May 27, 2013 in Algebra 2 Answers by anonymous | 1.4k views
Welcome to MathHomeworkAnswers.org, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
87,516 questions
100,344 answers
2,420 comments
762,751 users