What is the number from 100 to 1000 which can be divisible 2,3,4,5,6,7,8 and 9 and have a reminder of 1

There is none.

First factorize the numbers 2 to 9 into primes. Now work with the highest power of the primes 2, 3, 5 and 7 in those factorizations to solve x = 1 mod 8, x = 1 mod 9, x = 1 mod 5 and x = 1 mod 7.

Since 8, 9, 5, and 7 are prime powers then their product 5*7*8*9 = 2520 divides x-1, so x = 1 mod 2520.

Sure you have the right Q?

Least number = LCM of 2 to 9 + Remainder
= 2520 + 1 = 2521

Report Abuse