Question

Fill in the blank to create a two digit number the two digit number___1 is divided by 9
Answer
What single digit numbers besides one divide evenly into 24 and 96 list your responses in order from least lowest to highest numbers
How many numbers?
_,_,_,_
Answered by GPT-4o mini
To find a two-digit number in the form of "___1" that is divisible by 9, we can use the divisibility rule for 9: a number is divisible by 9 if the sum of its digits is divisible by 9.

Let's represent the two-digit number as "X1," where X is the tens digit (a single digit from 1 to 9).

The sum of the digits of the number X1 is X + 1. We need to find a value for X such that (X + 1) is divisible by 9.

The possible sums that are divisible by 9 within the range of digit sums (from the minimum 1 to maximum 18 for two-digit numbers) are:
- 9

Now, we can solve for X:
- X + 1 = 9
- X = 8

Thus, the two-digit number is "81."

The number 81 is divisible by 9, as 8 + 1 = 9, which is divisible by 9.

Therefore, the blank can be filled with 8: **81**.
Answered by GPT-4o mini
To find the single-digit numbers (besides 1) that divide evenly into both 24 and 96, we can first identify the single-digit integers (2 through 9) and then check which of these are divisors of both 24 and 96.

1. **Divisors of 24:**
- 1, 2, 3, 4, 6, 8, 12
- Single-digit divisors: 2, 3, 4, 6, 8

2. **Divisors of 96:**
- 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
- Single-digit divisors: 2, 3, 4, 6, 8

Now we can identify the common single-digit divisors of both 24 and 96:

- Common divisors: **2, 3, 4, 6, 8**

Thus, the single-digit numbers (besides 1) that divide evenly into both 24 and 96 are 2, 3, 4, 6, and 8.

**Ordered List:**
- 2, 3, 4, 6, 8

**Total Count:**
There are **5** numbers.

So, the final answer is:
2, 3, 4, 6, 8 (5 numbers)