DIVISIBILITY

Dr davis wants to divide 8487 tongue depressors evenly among some containers. she has 10 containers but does not need to use them all. how many containers could she use so there are no tongue depressors left over?

u sure?

i got 3

We're both right. However, if she only uses 3 containers, she'd have over 2800 tongue depressors in each. She'd have less than 1,000 in each of 9 containers.

ok thanks

You're welcome.

So 3 is the answer??

To find out how many containers Dr. Davis could use to divide the tongue depressors evenly, we need to determine the divisors of 8487. Divisors are the numbers that divide a given number evenly without leaving a remainder.

One approach to finding the divisors of 8487 is by performing prime factorization. By doing so, we can express 8487 as a product of prime numbers:

8487 = 3 * 3 * 7 * 11 * 23

Now, let's combine these prime factors differently to find divisors. We can choose any combination of prime factors as long as the exponent (number of times each prime factor is used) is between 0 and the maximum available exponent.

Starting with powers of 3, we can select the exponent from 0 to 2 because the highest exponent for 3 is 2:

Number of ways to select powers of 3: 3 (0, 1, 2)

Next, let's consider powers of 7, where we can select the exponent from 0 to 1 as the highest exponent for 7 is 1:

Number of ways to select powers of 7: 2 (0, 1)

Then, we move on to the powers of 11, which can only be 0:

Number of ways to select powers of 11: 1 (0)

Finally, for powers of 23, it can only be 0:

Number of ways to select powers of 23: 1 (0)

To obtain the total number of divisors, we multiply the number of choices for each prime factor:

Total number of divisors = 3 * 2 * 1 * 1 = 6

Therefore, Dr. Davis could use up to 6 containers to divide the 8487 tongue depressors evenly.