2006-11-12 21:23:16 · 5 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
"100 factorial". It means the product of all the whole numbers up to that number multiplied together. For example, 10! = 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 = 3,628,800. Note the two zeros at the end. 100! is a huge number, way too big for my calculator. But I know it ends with an even longer string of zeros. How many zeros are there at the end of 100 factorial? How about 1000!? (Hint: 10 = 2 x 5)
One hundred factorial (100!) is a huge number of 158 digits, but I know it ends with 24 zeros. We add a zero to the tail of a number whenever we multiply by 10, which is 2 x 5. There are lots of twos as factors of 100!, but not as many fives, so the number of zeros will be the same as the number of fives. The factors 5, 10, 15, 20, ... each contribute a five, and 25, 50, 75, and 100 each add an extra. So the total is 100 / 5 + 100 / 25 = 24. Calculators are handy, but they're not always the best tool for thinking about numbers!
hope that helps!!
2006-11-12 21:40:04 · answer #1 · answered by thesekeys 3 · 1⤊ 0⤋
2 from 100 and 1 from 95, 90, 85, 80, 75, 70, 65, 60, 55, 50, 45, 40, 35, 30, 25, 20, 15, 10, 5 (Any 5 by any even gives a trailing 0)
Hence 21 zeros trail 100!
Postscript: Whoops forgot about the extra zeros from 25, 50 and 75 so that's 3 more giving 24!!!!
2006-11-12 21:27:30 · answer #2 · answered by Wal C 6 · 2⤊ 1⤋
0 10 20 30 40 50 60 70 80 90 100
10 without including 100
12 with 100
2006-11-12 21:47:06 · answer #3 · answered by little_devil 2 · 1⤊ 4⤋
24,,
reason how many tiimes it is divisible by 10 or how many times by 2 and 5
number of 5's is much less than 2
20 numbers are dvisible by 5 so 20
4 numbers are dvisible by 5*5 so 4 more
non divisible by 5^3
so total 20+ 4= 24
number of 2's > 50
2006-11-12 21:27:21 · answer #4 · answered by Mein Hoon Na 7 · 4⤊ 0⤋
looks like 2 to me but what do I know?
2006-11-12 21:25:53 · answer #5 · answered by Anonymous · 0⤊ 4⤋