8. A way to work this out is figure out how many possible digits can go in each place value position (units, tens, hundreds) and multiply these together. Since there are 2 possible digits that can go in each position and there are three positions, you would go: 2 x 2 x 2 = 8 Want a list? 222 225 252 255 555 552 525 522
27 and 81; 27 + 81 = 108, and 3 x 27 = 81
There is no set of three consecutive integers for 187.
That isn't possible; three consecutive integers, or three consecutive positive integers, always have a sum that is a multiple of 3. In general, you can solve this quickly by trial and error. In this case, you will quickly find that a certain set of three consecutive integers will give you a sum that is TOO LOW, while the next-higher even integers will give you a sum that is TOO HIGH. You can also write an equation and solve it: n + (n + 2) + (n + 4) = 32. If you solve it, you will find that the solution is fractional, not integral.
9240 is the product of the three consecutive integers 20, 21, and 22.
Three of them.
17
Of the 729 numbers that satisfy the requirement of positive integers, 104 are divisible by 7.
997
To find the number of three-digit positive integers with digits whose product is 24, we can break down 24 into its prime factors: 2 x 2 x 2 x 3. The possible combinations for the three digits are (2, 2, 6), (2, 3, 4), and (2, 4, 3). These can be arranged in 3! ways each, giving a total of 3 x 3! = 18 three-digit positive integers.
The set of integers is divided into three subsets. One is the positive integers. Another is the negative integers. The last subset has one element -- zero. In sum, integers are composed of the positive integers, the negative integers, and zero.
31 + 62 + 93 + 13 + 26 + 39 = 264
The first three positive integers, 1, 2, and 3, satisfy this condition.
There can be only one.
Assuming that 001, 080, etc are not allowed (that is a leading zero or two is not permitted), the smallest number with exactly three digits is 100. The largest number with exactly three digits is 999. So there are 999 - 100 + 1 = 900 numbers with exactly three digits.
It may be either. If any of the integers is zero, the product will be zero. Else, if one or three of the integers is negative, the product will be negative. Otherwise, it will be positive.
1, 3 and 81 are three.