Question

The length of the Boston Marathon is 138,435 ft. Each stride, or step, by a particular runner is 3ft long. Does the number of strides the runner takes fit evenly into the length of the race? Explain

Answer 1

Just add up all the individual digits and if the result is divisible by 3 then the original number is also.

Answer 2

By evenly the problem means that if you layed all the strides side by side, then the last one would end exactly on the finish line. Or more simply, if you divide the course length by the stride, the Remainder would be zero. There are no even or odd groups to worry about.

So 138,435 / 3 = 46,145 strides exactly, so the strides fit evenly into the course.
I could have a stride of 3.2 ft and win the race even though 138,435 / 3.2 = 43,260.9375 doesn't fit evenly. Then my last stride would land beyond the finish line and not just on it.

Answer 3

can you help with more? @karolynxx

Answer 4

What else maybe I can help @rainbowswirl

Answer 5

I'm still confused @karolynxx

Answer 6

ok thanks @Osgood

Answer 7

A number is written with the following factorization: 2 to the 2nd power x 3 x 5 to the 4th power x 8 x 11 to the 2nd power. Is this factorization a prime factorization. Explain why or why not. If it is not correct, give the correct prime factorization of the number. @Osgood @karolynxx

Answer 8

@xMissAlyCatx

Answer 9

IDK @rainbowswirl but @xMissAlyCatx will probably know I have to go

Answer 10

oh, okay. I really need help @Osgood @xMissAlyCatx

Answer 11

What @karolynxx said was pretty solid, though.

Answer 12

Did you see my other question? I figured out the one @karolynxx did. Could you help me? @xMissAlyCatx

Answer 13

I could have a stride of 3.2 ft and win the race even though 138,435 / 3.2 = 43,260.9375 doesn't fit evenly. Then my last stride would land beyond the finish line and not just on it i put that on there

Answer 14

I dont get it @xMissAlyCatx

Answer 15

i see what your asking

Answer 16

The sum of the digits is: 24.

This, the number is divisible by 3.

Additionally, we know 120,000 is divisible by 3, 18,000 is divisible by 3, 420 is divisible by 3, and 15 is divisible by 3. so 3

Answer 17

I think I got that one down @karolynxx. could you help with more though?

Answer 18

Is it a prime factorization though? @karolynxx

Answer 19

Hey @rainbowswirl This site will describe prime factorization
http://www.mathsisfun.com/prime-factorization.html