4th Grade Common Core Math Worksheets - Free Printable

Here are the solutions to the problems on the worksheet.

1. Use the arrays below to find the factors of 18.
To find the factors, we look at how many rows and columns are in each rectangle (array).
* a. The first array is a single long row. It has 1 row and 18 columns. So, $1 \times 18 = 18$.
* b. The second array has 2 rows and 9 columns. So, $2 \times 9 = 18$.
* c. The third array has 3 rows and 6 columns. So, $3 \times 6 = 18$.

Solution:
a. 1 and 18
b. 2 and 9
c. 3 and 6

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2. Use additional blank paper to draw arrays to find the factors.
We need to find pairs of numbers that multiply together to make the target number.
* a. 9: $1 \times 9$ and $3 \times 3$. Factors: 1, 3, 9.
* b. 17: This is a prime number. Only $1 \times 17$ works. Factors: 1, 17.
* c. 26: $1 \times 26$ and $2 \times 13$. Factors: 1, 2, 13, 26.
* d. 36: $1 \times 36$, $2 \times 18$, $3 \times 12$, $4 \times 9$, $6 \times 6$. Factors: 1, 2, 3, 4, 6, 9, 12, 18, 36.
* e. 42: $1 \times 42$, $2 \times 21$, $3 \times 14$, $6 \times 7$. Factors: 1, 2, 3, 6, 7, 14, 21, 42.
* f. 55: $1 \times 55$ and $5 \times 11$. Factors: 1, 5, 11, 55.
* g. 68: $1 \times 68$, $2 \times 34$, $4 \times 17$. Factors: 1, 2, 4, 17, 34, 68.
* h. 72: $1 \times 72$, $2 \times 36$, $3 \times 24$, $4 \times 18$, $6 \times 12$, $8 \times 9$. Factors: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.

Solution:
a. 1, 3, 9
b. 1, 17
c. 1, 2, 13, 26
d. 1, 2, 3, 4, 6, 9, 12, 18, 36
e. 1, 2, 3, 6, 7, 14, 21, 42
f. 1, 5, 11, 55
g. 1, 2, 4, 17, 34, 68
h. 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

***

3. Write the first 10 multiples of the following numbers.
To find multiples, you multiply the number by 1, then 2, then 3, all the way to 10.
* a. 9: $9\times1=9$, $9\times2=18$, $9\times3=27$, $9\times4=36$, $9\times5=45$, $9\times6=54$, $9\times7=63$, $9\times8=72$, $9\times9=81$, $9\times10=90$.
* b. 10: $10, 20, 30, 40, 50, 60, 70, 80, 90, 100$.
* c. 11: $11, 22, 33, 44, 55, 66, 77, 88, 99, 110$.

Solution:
a. 9, 18, 27, 36, 45, 54, 63, 72, 81, 90
b. 10, 20, 30, 40, 50, 60, 70, 80, 90, 100
c. 11, 22, 33, 44, 55, 66, 77, 88, 99, 110

***

4. List the numbers that are multiples of 6, but are not factors of 30 and, are less than 60.
First, let's list the multiples of 6 that are less than 60:
6, 12, 18, 24, 30, 36, 42, 48, 54.

Next, let's identify the factors of 30 (numbers that divide into 30 evenly):
1, 2, 3, 5, 6, 10, 15, 30.

Now, we remove any number from our "multiples of 6" list that appears in the "factors of 30" list.
* 6 is a factor of 30. (Remove it)
* 30 is a factor of 30. (Remove it)

The remaining numbers are: 12, 18, 24, 36, 42, 48, 54.

Solution:
12, 18, 24, 36, 42, 48, 54

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5. Kevin has \$25 to buy a toy car. The price of the toy cars is a multiple of \$4. What are the possible prices of toy cars?
Kevin can spend up to \$25. We need to find multiples of 4 that are less than or equal to 25.
* $4 \times 1 = 4$
* $4 \times 2 = 8$
* $4 \times 3 = 12$
* $4 \times 4 = 16$
* $4 \times 5 = 20$
* $4 \times 6 = 24$
* $4 \times 7 = 28$ (This is too much money!)

Solution:
\$4, \$8, \$12, \$16, \$20, \$24

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6. Which list contains all the factors of 27?
Let's find the factors of 27:
* $1 \times 27 = 27$
* $3 \times 9 = 27$
The factors are 1, 3, 9, and 27.

Let's check the options:
A. Missing 1.
B. Includes 18, which is not a factor ($27 \div 18$ is not a whole number).
C. Includes 2, which is not a factor (27 is odd).
D. Has 1, 3, 9, 27. This is correct.

Solution:
D

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7. Which number is not a multiple of 6?
A multiple of 6 must be divisible by both 2 (it must be even) and 3 (the digits add up to a multiple of 3). Or simply, check if it is in the 6 times table.
* C. 6 ($6 \times 1$) - Yes, it is a multiple.
* D. 12 ($6 \times 2$) - Yes, it is a multiple.
* C. 16 - Let's check: $16 \div 6 = 2$ with a remainder of 4. It is not a multiple.
* D. 30 ($6 \times 5$) - Yes, it is a multiple.

Solution:
C