2006-09-30 10:57:20 · 7 answers · asked by clara 1 in Science & Mathematics ➔ Mathematics
oh and...what does the ! mean?
2006-09-30 11:25:59 · update #1
your right I meant superscript 2^x
2006-09-30 11:47:26 · update #2
2^x divides 10!
2006-09-30 11:49:07 · update #3
I assume you mean "superscript", not "subscript". Then the question is, what is the largest x such that 2^x (2 to the power x) divides 10! (not "divides by").
To answer this, look at the prime factorization of each of the numbers 1 through 10. Only the even numbers are divisible by 2, so we restrict ourselves to those. You have 2, then 4 = 2*2, then 6 = 2*3, 8=2*2*2, and 10=2*5. There are 8 factors of 2 altogether, so x=8. 10! is divisible by 2^8 = 256.
2006-09-30 11:40:42 · answer #1 · answered by James L 5 · 0⤊ 0⤋
I think you mean the largest x such that 2^x divides 10!
Count all the different exponents of 2 in the product and add them.
10 1
8 3
6 1
4 2
2 1
Total: 8
So 2^8||10!
2006-09-30 11:15:34 · answer #2 · answered by steiner1745 7 · 0⤊ 0⤋
The factors of 2^x are all powers of 2, therefore there are no 2^x numbers that divide 10!.
2006-09-30 11:04:43 · answer #3 · answered by Anonymous · 0⤊ 0⤋
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2016-12-15 17:30:37 · answer #4 · answered by ? 3 · 0⤊ 0⤋
Let 2^x/10!= 1
Taking log both sides
x log 2 = log 10!
x = log10!/log 2=21.79106119
Therefore x =21.79106119
2006-09-30 13:00:33 · answer #5 · answered by Amar Soni 7 · 0⤊ 1⤋
the questions is not clear
2006-09-30 10:59:59 · answer #6 · answered by raj 7 · 0⤊ 0⤋
having problems with your homework...?
2006-09-30 11:04:41 · answer #7 · answered by HoTbOd sWiMmeR 2 · 0⤊ 0⤋