Factorial seconds

The number of weeks in $10!$ seconds =

$\dfrac {10!} {60 \ \times 60 \times 24 \times 7} = \dfrac { 2^8 \times 3^4 \times 5^2 \times7 } {2^7 \times 3^3 \times 5^2 \times 7 } = 2 \times 3 = \boxed{6}$

(10!)/week =(10!) / (days x hours x minutes x seconds) =(10!) / (7x24x60x60) =(10!) / [7x(3x8)x(3600)] =(10!) / [7x3x8x(4x9x10x2x5)] =(10x9x8x7x6x5x4x3x2x1) / (10x9x8x7x5x4x3x2) =6x1 = 6

10!÷7×24×60×60

I would use dimensional analysis 10! = (10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2) sec x (1 min)/(60 sec) gives 9 x 8 x 7 x 5 x 4 x 3 x 2 min (9 x 8 x 7 x 5 x 4 x 3 x 2 min) x (1 hr)/(60 min) gives 9 x 8 x 7 x 2 hrs (9 x 8 x 7 x 2) hrs x (1 day)/(24 hrs) gives (3 x 7 x 2) days (3 x 7 x 2) days x (1 week)/(7 days) gives 3 x 2 = 6

best way is to go on cutting terms from factorial 10...first off, 24 is fact.4 so 4x3x2x1 are gone from numerator, then cut 7...now we're left with 10 9 8 6 and 5 in numerator and 3600 in the denom....5x6=30 / 3600 = 1/120.... cut 10x9x8 by 120....answer is 6

one week in seconds is

7 (days in a week) x 24 (hours in a day) x 3600 (seconds in a hour)

so we have

7x(3x8)x(36x100) seconds in a week.

Using a comfortable factorization . 36 = 9x4 and 100 = 2x5x10 so the seconds are

7x3x8x9x4x2x5x10 = (ordering by growing factors) = 2x3x4x5x7x8x9x1x0 = (10!)/6

And trivially the answer is 6 without any calculation,

compute what 10! = 3628800. Then there are 60 seconds in 1 minute and 60 minutes in 1 hour and 24 hours in 1 day. To get how many seconds in 1 day multiply 60 seconds times 60 minutes times 24 hours to get 86400. Then divide 10! by 86400 to get 42, then there are 7 days in a week divide 42 by 7 to get 6.

10!/7/24/60/60=6

I just did something easy. Figured out what 10! was on a Google calculator, then divided by 60 to change from seconds to minutes, divide by 60 again to change from minutes to hours, divide by 24 to change from hours to days, then divide by 7 to change days to weeks. It's what everyone's saying, but doing it all 1 at a time makes it a little easier to follow.

$\frac { 10\cdot 9\cdot 8\cdot 7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2 }{ 7\cdot 4\cdot 6\cdot 6\cdot 10\cdot 6\cdot 10 } =\frac { 10\cdot 5\cdot 2 }{ 10\cdot 10 } \cdot \frac { 9\cdot 8\cdot 3 }{ 6\cdot 6\cdot 6 } \cdot \frac { 7\cdot 4 }{ 7\cdot 4 } \cdot 6=6$

Factorization works: Ensuring units cancel

Number of weeks = (10! secs) * (1 min/60sec) * (1 hrs/60min) * (1 day/24hrs) * (1weeks/7 day) = (10! weeks) / ( 60 * 60 * 24 * 7) = (10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 weeks) / ((10 * 6)(5 * 4 * 3)(8 * 3)(7))

Rearrange in descending order for clarity: = (10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 weeks) / (10 * 8 * 7 * 6 * 5 * 4 * 3 * 3)

Cancelling common factors = (9*2 weeks) / (3) = 6 weeks ===>

10 9 8 7 6 5 4 3 2 1 =[ 7 (6 10) (5 4 3) (8 3)] 3 2 which leaves 6.

We first note that $10! seconds$ is equal to

$10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1$ seconds.

The 1 changes nothing and can be removed to get

$10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2$ seconds.

To change seconds to minutes, we divide by $60$ . This cancels with the $6$ and $10$ , so we have

$9 \times 8 \times 7 \times 5 \times 4 \times 3 \times 2$ minutes.

Now we need to change minutes to hours, for which we again divide by $60$ . We can cancel this with the $5$ , the $4$ , and the $3$ to get

$9 \times 8 \times 7 \times 2$ hours.

To change to days, we need to divide by $24$ . We can cancel with the $8$ and the $9$ . We're dividing the $9$ by $3$ , as we don't have any other $3$ s to cancel. This gives us

$3 \times 7 \times 2$ days.

Finally, we have to divide by $7$ to get weeks, and we cancel to get

$3 \times 2$ weeks.

This simplifies to our final answer of

$\boxed{6}$ weeks.

(1x2x3x4x5x6x7x8x9x10)/(60x60x24x7) = 6

10! seconds = 10 9 8 7 6 5 4 3 2*1 = 3628800 seconds.

Seconds in a week:

3600 second in an hour.

3600*24 h = 86400 seconds in a day.

86400 * 7 days a week = 604800 seconds in a week.

therefore : 3628800/604800 = 6 weeks.

We had to memorize factorials up to 10 in class for homework:

3! = 6

4! = 24

Knowing these of the tops of our heads, we can use them to limit the amount of work needed to be done.

$\frac{10!}{3! * 10 * 3! * 10 *4! *7}$

This is to convert seconds to weeks. 60 is also equal to 3! * 10, so divide it by this twice to get minutes, then hours. We know 4! is 24, so dividing this way will get us the number of days. Then, divide by 7 to get weeks. Lastly, because dividing by a, b and c is the same as dividing by the product of a, b and c, we can multiply them all and divide, rather than dividing in several steps.

= $\frac{10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1}{3 *2 * 1 * 10 * 3 * 2 * 1 * 10 * 4 * 3 * 2 * 1 * 7}$

After this, we can easily simplify, leaving us with only 6 in the numerator and three ones in the denominator.

easy way!!! 60/10=6>>>>>>>>60 min and 10 sec converting it we get 6 its EASy

1minute=60seconds 60480minutes=10!seconds

1hour=60minutes 1008hours=60480minutes

1day=24hours 42days=1008hours

1week=7days 6weeks=42days

10!÷7×24×60×60 =7