To solve this, we need to find an integer $d$ that:

1. Divides $15$, meaning $15 \div d$ results in an integer.
2. Does not divide $25$, meaning $25 \div d$ does not result in an integer.

Step 1: Determine the divisors of 15

The divisors of $15$ are: $1, 3, 5, 15$

Step 2: Determine the divisors of 25

The divisors of $25$ are: $1, 5, 25$

Step 3: Compare the sets

We need a divisor of $15$ that is not a divisor of $25$. From the lists above:

• Divisors of $15$: $1, 3, 5, 15$
• Divisors of $25$: $1, 5, 25$

The only divisor of $15$ that does not appear in the divisors of $25$ is: $\boxed{3}$

Verification

• $15 \div 3 = 5$, so $3$ divides $15$.
• $25 \div 3 \neq$ integer, so $3$ does not divide $25$.

Thus, $\boxed{3}$ is the integer $d$ that satisfies the conditions.

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Would you like more details or have any further questions? Here are 5 related questions to deepen your understanding:

1. Can you list all integers $d$ that divide $15$ but not $25$?
2. Why does $3$ divide $15$ but not $25$?
3. What is the least common multiple (LCM) of $15$ and $25$?
4. How do the prime factorizations of $15$ and $25$ relate to their divisors?
5. Can you apply similar logic to find divisors of other pairs of numbers?

Tip: Always compare the sets of divisors when solving problems like this to isolate differences efficiently!