Which is the smallest number, with which if you divide by 10 you get 9 as reminder, divide by 9 you get 8 as reminder, divide by 8 you get 7 as reminder and likewise upto if you divide by 2 you get 1 as reminder ?
Lets say the number is X. So X+1 would a number that is divisible by 10, 9, 8, 7, 6, 5, 4, 3, 2 and 1. This is same as 10!. However 10! has many repeating factors, which need to be removed.
10 X 9 X 8 X 7 X 6 X 5 X 4 X 3 X 2 X 1 = (2 X 5) X (3 X 3) X (2 X 2 X 2) X 7 X (2 X 3) X 5 (2 X 2) X 3 X 2 X 1 Removing the repeating factors we shall be left with: a. 3 X 3 (This takes care of 9 and 3) b. 2 X 2 X 2 (This takes care of 8, 4, 2 and alos one of the factors of 10) c. 7 d. 5 e. 1
So by multiplying all these together we get 3 X 3 X 2 X 2 X 2 X 7 X 5 X 1 = 2520
So 2520 is the lowest number that is divisible by 10, 9, 8, 7, 6, 5, 4, 3, 2 & 1.
Therefore 2520 -1=2519 is the number that when divide by 10 you get 9 as reminder, divide by 9 you get 8 as reminder, divide by 8 you get 7 as reminder and likewise upto if you divide by 2 you get 1 as reminder.
Lets say the number is X. So X+1 would a number that is divisible by 10, 9, 8, 7, 6, 5, 4, 3, 2 and 1. This is same as 10!. However 10! has many repeating factors, which need to be removed.
ReplyDelete10 X 9 X 8 X 7 X 6 X 5 X 4 X 3 X 2 X 1 =
(2 X 5) X (3 X 3) X (2 X 2 X 2) X 7 X (2 X 3) X 5 (2 X 2) X 3 X 2 X 1
Removing the repeating factors we shall be left with:
a. 3 X 3 (This takes care of 9 and 3)
b. 2 X 2 X 2 (This takes care of 8, 4, 2 and alos one of the factors of 10)
c. 7
d. 5
e. 1
So by multiplying all these together we get 3 X 3 X 2 X 2 X 2 X 7 X 5 X 1 = 2520
So 2520 is the lowest number that is divisible by 10, 9, 8, 7, 6, 5, 4, 3, 2 & 1.
Therefore 2520 -1=2519 is the number that when divide by 10 you get 9 as reminder, divide by 9 you get 8 as reminder, divide by 8 you get 7 as reminder and likewise upto if you divide by 2 you get 1 as reminder.