A four digit number

I am a student. Need to find a 4 digit number that can be divided by 2, 3, 4, 5, 6, 7, 8, 9, and will always have a remainder of 1 in the answer.

Hi Dean,

First look for a four digit number that gives a remainder of zero in each case and then add one to get remainders of one. What you are then looking for is the least common multiple (LCM) of 2, 3, 4, 5, 6, 7, 8 and 9. Begin by finding the prime factors of each nine numbers.

2 = 2¹
3 = 3¹
4 = 2²
5 = 5¹
6 = 2¹3¹
7 = 7¹
8 = 2³
9 = 3²

Looking at the highest power of each prime in the list above, the least common multiple is

2³ 3² 5 7 = 2520 Thus the number that you want is 2520 + 1 = 2521. You should now check with each of the digits from 2 to 9 to ensure that the remainder is always 1.

Cheers,
Penny Go to Math Central