4th Grade · 4.OA.B.4

Prime and composite numbers in 4th grade

Prime and composite numbers are two kinds of whole numbers, sorted by how many ways they can be made by multiplying. In 4th grade, your child finds all the factor pairs of a number up to 100. Your child then uses them to decide whether the number is prime or composite.

What the standard says

The official Common Core wording, quoted exactly. The plain version follows.

4.OA.B.4 Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite.

What it means, in plain words

A factor pair is two whole numbers that multiply to make a number. The factor pairs of 12 are $1 \times 12$ , $2 \times 6$ and $3 \times 4$ . With 12 square tiles, your child can build three different rectangles that match these pairs. Each number in a factor pair is a factor of 12.

Factors and multiples are the same fact seen from opposite ends. 3 is a factor of 12, and 12 is a multiple of 3. The multiples of 3 are the numbers you say when you skip count by 3: 3, 6, 9, 12, 15 and so on. Your child also checks whether a number up to 100 is a multiple of a one-digit number. For example, 72 is a multiple of 8, because $8 \times 9 = 72$ .

A prime number has exactly two factors, 1 and the number itself, so it has only one factor pair. 7 is prime: the only way to make it is $1 \times 7$ , and 7 tiles make only one long row. A composite number has more than two factors, as 12 does. The number 1 is neither prime nor composite, because its only factor is 1. The work on prime and composite numbers in 4th grade uses numbers from 1 to 100.

Your child should be able to:

Find all the factor pairs of a whole number up to 100
Explain that a number is a multiple of each of its factors
Decide whether a number up to 100 is a multiple of a one-digit number
Sort a number up to 100 as prime or composite

Example

What are all the factor pairs of 36? Is 36 prime or composite?

Start at 1 and go up: $1 \times 36$ , $2 \times 18$ , $3 \times 12$ and $4 \times 9$ all make 36.
5 does not work, because 36 is not a multiple of 5. Then $6 \times 6 = 36$ .
The next factor is 9, and $9 \times 4$ is a pair already found, so the list is done.
The factor pairs of 36 are $1 \times 36$ , $2 \times 18$ , $3 \times 12$ , $4 \times 9$ and $6 \times 6$ . 36 has more than one factor pair, so it is composite.

Example

Is 29 prime or composite?

Try the numbers from 2 up. 29 is not a multiple of 2, 3, 4 or 5.
There is no need to go further, because $6 \times 6 = 36$ is already more than 29.
The only factor pair is $1 \times 29$ , so 29 is prime.

Where children usually get stuck

Asked for the factors of 8, your child writes 8, 16, 24.
Factors and multiples describe one relationship from opposite ends, and neither word says which direction it goes in everyday English.
What helps. Ask which numbers multiply to make 8. Those are the factors (1, 2, 4 and 8), and none is bigger than 8. The skip-count numbers 8, 16, 24 are the multiples.
Your child says 1 is a prime number.
The common definition, "a number divisible only by 1 and itself", fits 1. The child is following the definition more carefully than it was written.
What helps. Use the clearer definition: a prime number has exactly two different factors. Ask how many factors 1 has. It has only one, so it is not prime.
Your child says 51 is prime, because it is odd and does not end in 5.
51 is not in the times tables up to 10, so it looks like it has no factors. Odd numbers that do not end in 5 can still have factors such as 3 or 7.
What helps. Skip count by 3 together, or work out $51 \div 3$ . It comes out even, because $3 \times 17 = 51$ , so 51 is composite.

Try four practice questions

Real 4th grade questions from our question bank, easiest first. Answer them right here, check each one, and see a worked solution for any question.

1Warm-up
Is 2 a factor of 14?
$\displaystyle 2 \times \underline{\phantom{00}} = 14$
A
Yes
B
No
Show the answer and how to solve it
$2$ is a factor of $14$ because $2 \times 7 = 14$ exactly.
1. 1We need to find a whole number that fills the blank to make $2 \times ? = 14$ true.
2. 2Try multiples of $2$ close to $14$ :
3. 3Since $2 \times 7 = 14$ exactly, $2$ is a factor of $14$ . The answer is Yes.
Common mistake. A common mistake is thinking $2$ is not a factor because the pair $2 \times 7 = 14$ is not a basic multiplication fact. You can still check by trying multiples until you reach $14$ .
The idea underneath. A number is a factor of $14$ only when multiplying it by a whole number gives EXACTLY $14$ . Near-products do not count.
2On level
Select all the numbers below that are multiples of $4$ .
A
8
B
14
C
20
D
36
E
57
Show the answer and how to solve it
The multiples of $4$ in the list are $8$ , $20$ , and $36$ , because $4 \times 2 = 8$ , $4 \times 5 = 20$ , and $4 \times 9 = 36$ .
1. 1A multiple of $4$ is a number you reach by counting by $4$ (skip-counting by $4$ ). The first several multiples of $4$ are:
2. 2Check each number in the list to see if it is in the $4$ skip-count.
3. 3The numbers that are multiples of $4$ are $8$ , $20$ , and $36$ .
Common mistake. A common mistake is selecting $14$ because it is close to $12$ (a multiple of $4$ ). But $14$ is not a multiple of $4$ — the $4$ skip-count jumps from $12$ to $16$ , skipping past $14$ .
The idea underneath. A multiple of $4$ must be in the $4$ skip-count. Skip-counting lets you check membership without testing divisibility.
3On level
List all the factors of 12. Type each factor in order from smallest to largest.
Show the answer and how to solve it
The factors of 12 from smallest to largest are 1, 2, 3, 4, 6, and 12.
1. 1Check whole numbers in order, starting with 1. A number is a factor when a whole number times it equals 12.
2. 2We checked 1 through 3. If both factors were 4 or larger, their product would be at least $4\times4=16$ , which is too large. Any remaining factor must pair with a number we already checked, so it cannot give a new pair.
3. 3Collect both numbers from each pair. From smallest to largest, the factors are 1, 2, 3, 4, 6, and 12.
Common mistake. Include both numbers from each pair. For example, $3\times4=12$ means that both 3 and 4 belong in the list.
The idea underneath. A factor pair is two whole numbers that multiply to make the target number. Each number in the pair is a factor.

4Stretch

Aiden wants to list every factor pair of 48. His list is shown below. Select the statement that best describes the list.

\displaystyle 1 \times 48 = 48

\displaystyle 2 \times 24 = 48

\displaystyle 3 \times 16 = 48

\displaystyle 16 \times 3 = 48

\displaystyle 4 \times 12 = 48

\displaystyle 6 \times 8 = 48

The list includes a pair whose product is not 48.

The list is missing a factor pair.

The list is complete and correct.

The list counts the same factor pair twice by reversing the order.

Show the answer and how to solve it

Aiden's list shows $3 \times 16 = 48$ and $16 \times 3 = 48$ — the same factor pair written in reversed order. The best description is that the list counts the same factor pair twice by reversing the order.

1Look at Aiden's list.
2Find every factor pair of $48$ by checking each whole number starting at $1$ . A number is a factor when it divides $48$ evenly:
3Compare with Aiden's list. The pairs $3 \times 16$ and $16 \times 3$ are the same factor pair listed twice — the order of factors does not matter.
4Aiden's list counts the same factor pair twice by reversing the order.

Common mistake. A common mistake is treating $3 \times 16$ and $16 \times 3$ as two different factor pairs. Since the order of factors does not matter, $3 \times 16$ and $16 \times 3$ count as one factor pair and should only appear once.

The idea underneath. $3 \times 16$ and $16 \times 3$ use the same two factors written in a different order — they count as one factor pair. Every factor pair can be found by checking each whole number from $1$ in order: when a number divides $48$ evenly, it pairs with the quotient to form a factor pair.