Factors & Multiples - Pre Algebra

1. What is the divisibility rule for $3$?

   A whole number is divisible by $3$ when the sum of its digits is divisible by $3$.

2. What is the smallest multiple of $6$ that is greater than $50$?

   $54$. The multiples near $50$ are $48$ and $54$.

3. What are the first four positive multiples of $7$?

   $7, 14, 21, 28$. Multiply $7$ by $1, 2, 3$ and $4$.

4. What is the divisibility rule for $4$?

   A whole number is divisible by $4$ when the number formed by its last two digits is divisible by $4$.

5. What are all the factors of $18$?

   $1, 2, 3, 6, 9, 18$. They come in pairs: $1 \times 18$, $2 \times 9$, $3 \times 6$.

6. What is a multiple of a whole number?

   The product of that number and a whole number. For example, $12$ is a multiple of $4$ because $4 \times 3 = 12$.

7. How many factors does $16$ have?

   $5$: $1, 2, 4, 8, 16$. The pair $4 \times 4$ counts $4$ only once.

8. What is the greatest factor of $45$ that is less than $45$?

   $15$. The smallest factor greater than $1$ is $3$, and $45 \div 3 = 15$.

9. Which of $6$, $8$ and $9$ is a factor of $84$?

   $6$, since $84 \div 6 = 14$. Dividing $84$ by $8$ or by $9$ leaves a remainder.

10. What is a factor of a whole number?

    A whole number that divides it with no remainder. For example, $4$ is a factor of $12$ because $12 \div 4 = 3$.

11. Since $5$ is a factor of $35$, what is $35$ in relation to $5$?

    $35$ is a multiple of $5$. If $a$ is a factor of $b$, then $b$ is a multiple of $a$.

12. Which of $234$, $245$ and $251$ is divisible by $9$?

    $234$. Its digit sum is $2 + 3 + 4 = 9$; the others have digit sums $11$ and $8$.

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