The least common multiple of 6 and 8 is 24. Every multiple of 24 thus has a remainder of 0 when divided by 6 and when divided by 8.
For similar reasons, numbers that are 1 to 5 more than a multiple of 24 have remainders of 1 to 5 when divided by either 6 or 8.
We thus find numbers that are within 5 of a multiple of 24, between 101 and 199. There are four multiples of 24 in that range -- 120, 144, 168, and 192. That gives us 24 numbers with the same remainder upon division by 6 or 8. In addition, 101 is 5 more than 96, a multiple of 24. It thus works as well. This gives a total of 25 numbers.
No comments:
Post a Comment