Any mathematic brain boxes out there?

Question

My friends neice in 1st year got this home in her homework, can u help me, PLEASE?


What number, if divided by 2,3,4,5 and 6, leaves a remainder of 1, but not if divided by 7. 7 leaves it with no remainder.

Serious answers only please!

Thanx 2 all u who provide the workings of the sum, but none of u seem to carry it on 2 the stage of 7x. If memory serves, Nathan, u seemed to multiply/divide, until u got to 7 then u changed 300 into 301, so i dont think u r rite !!!!

Answer 1

Actually; Nathan, Chris_ninety1 and some others are right.
What you need is a multiple of 7, but an odd one, so start at 7 and add 14 to get every odd multiple until you get one that leaves a remainder of 1 with all the others.
Repeating like this eventually gets 301 as a multiple of 7.

300 is divisible by 2,3,4,5 and 6; so 301 would leave a remainder of 1 with each of these numbers; and is a multiple of 7.

The answer is therefore 301 - well done guys.

Answer 2

If it divides by 5 and leaves remainder 1, then it has to end in a 6 or a 1. Easy enough.

If it divides by 2 and leaves remainder 1, it has to be an odd number so the last digit must be the aforementioned 1.

It's not 21 or 91, or 161 or 231. Try 301.

*edit* Yep, definitely 301.

300/2 = 150
300/3 = 100
300/4 = 75
300/5 = 60
300/6 = 50

God am I good.

Answer 3

Actually, there are infinitely many numbers satisfying
the given condition. I'll show you how to find the smallest
one and then indicate how to find the rest.
Let x be the number we are seeking.
Then x-1 is divisible by 2,3,4,5,6, so it is divisible
by their least common multiple, which is 60.
Thus x-1 = 60k for some whole number k.
So x = 1 + 60k.
Now try the different values of k till you
find a number divisible by 7.
This turns out to be k = 5, so the smallest
number satisfying the conditions of the problem
is 301.
Finally, it can be proved that all the other
numbers k which work are of the form 5 + 7t
for whole numbers t. Thus the next
one is 60(12) +1 or 721.
Hope that helps your friend's niece!

Answer 4

The answer is 301

301 minus the remainder 1 is 300, then the following sums show the rest of the divisors...

300/6 = 50, 300/5 = 60, 300/4 = 75, 300/3 = 100, 300/2 = 150

301/7 = 43

there is your answer!!

Answer 5

It sounds like 61!

61/2 = 30 remainder 1
61/3 = 20 remainder 1
61/4 = 15 remainder 1
61/5 = 12 remainder 1
61/6 = 10 remainder 1

Answer 6

10 and 49 are not correct. If you divide 10 by 2 you get 5 with no remainder. If you divided 49 by 5, you get 9 with a remainder of 4. Unfortunately, I don't know how to get the answer other than testing an array of numbers.

Answer 7

yeah, its a multiple of 7

if you divide by 2 it has a remainder of 1 so you're looking for an odd number

if you divide by 5 you get reainder 1, so the answer either ends in 1 or 6, but can't end in 6 since you want an odd number, so it ends in 1

Answer 8

10

Answer 9

91

Answer 10

Try 49
49/7=7
49/6= 8r1
49/2= 24r1