4th Grade Factors, Multiples, Prime and Composite Worksheet Answer Key (PDF)

Q: How many factors does 36 have?

The number 36 has nine factors: 1, 2, 3, 4, 6, 9, 12, 18, and 36. Also, the factor pairs are 1 and 36, 2 and 18, 3 and 12, 4 and 9, and 6 and 6. The pair 6 and 6 counts the factor 6 only once.

Q: How do I find the mystery prime in problem 19?

List the primes between 40 and 50: 41, 43, and 47. Then find the one whose digits add to 11. For 47, 4 plus 7 is 11, so the mystery prime is 47. The other two sum to 5 and 7.

4th grade factors and multiples worksheet answers – Maths PDF

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This 4th grade factors and multiples worksheet answers covers factors, multiples, prime and composite (Common Core 4.OA.B.4), with a free PDF to print.

Key takeaway: Also, this answer key helps fourth grade students and parents check factor, multiple, prime, and composite work with every step shown.

Topic: Factors, Multiples, Prime and Composite (4th grade)
Content: Step-by-step answers to 20 worksheet problems
Standards: 4.OA.B.4
Answers: Every step shown, with the method to review
Format: Free printable PDF, US Letter, black and white

Also, this answer key helps fourth grade students and parents check factor, multiple, prime, and composite work with every step shown. Each solution lists factor pairs in order, so students can see how complete a list needs to be.

Then, the key covers all 20 problems, including the array in problem 4, the number line in problem 8, and the reasoning about Ethan’s claim in problem 20. Also, word problem answers explain how the factors or multiples fit the story. Compare your lists carefully, since a missing factor is the most common error. Then, plan about 15 minutes to check and fix your work.

Use this answer key to check each solution on the factors and multiples worksheet. Every problem shows the factor pairs or the skip counting used, so students can find any mistake and fix it.

Grade 4 · Common Core State Standards: 4.OA.B.4

4th grade factors and multiples worksheet answers: worksheet problems 1 to 10

1 – Factor pairs of 12

Next, Try each number from 1 up: \(1 \times 12 = 12\), \(2 \times 6 = 12\), \(3 \times 4 = 12\). Next, 4 is already used, so stop.

So, factor pairs: 1 and 12, 2 and 6, 3 and 4.

2 – Factors of 18

In addition, Pairs: \(1 \times 18\), \(2 \times 9\), \(3 \times 6\). 4 and 5 do not divide 18 evenly, and 6 is already listed.

Now, Factors: 1, 2, 3, 6, 9, 18.

3 – Multiples of 7

So, Skip count by 7: 7, 14, 21, 28, 35, 42.

Also, check: \(7 \times 6 = 42\). So, the multiples are 7, 14, 21, 28, 35, 42.

4 – Reading an array

Then, there are 5 rows of 6 tiles: \(5 \times 6 = 30\).

Next, factor pairs of 30: \(1 \times 30\), \(2 \times 15\), \(3 \times 10\), \(5 \times 6\).

Two of the four arrays that make 30.

Answer: \(5 \times 6 = 30\); pairs 1 and 30, 2 and 15, 3 and 10, 5 and 6.

Worksheet problem 5 and after

5 – Is it a factor?

In addition, divide: \(54 \div 6 = 9\) with no remainder, or \(6 \times 9 = 54\).

Yes, 6 is a factor of 54.

6 – Is it a multiple?

(a) \(8 \times 7 = 56\), so 56 is a multiple of 8.

(b) \(8 \times 7 = 56\) and \(8 \times 8 = 64\), so 58 falls between two multiples.

Answer: (a) yes, (b) no.

7 – Multiples of 4 in a list

Now, check each: \(4 \times 5 = 20\), \(4 \times 8 = 32\), \(4 \times 11 = 44\). The numbers 14, 26 and 38 leave a remainder of 2 when divided by 4.

So, Multiples of 4: 20, 32, 44.

8 – Missing multiples

Also, each jump is 8. After 16 comes \(16 + 8 = 24\). After 32 comes \(32 + 8 = 40\). After 56 comes \(56 + 8 = 64\).

All ten multiples of 8 up to 80.

Then, Missing numbers: 24, 40, 64.

Worksheet problem 9 and after

9 – Prime or composite

7 has factors 1 and 7 only: prime. 9 has factors 1, 3, 9: composite. 11 has factors 1 and 11 only: prime. 15 has factors 1, 3, 5, 15: composite.

Answer: 7 prime, 9 composite, 11 prime, 15 composite.

10 – Primes from 20 to 40

Next, Remove the even numbers and the multiples of 5. Then test the rest: 21 = \(3 \times 7,\) 27 = \(3 \times 9,\) 33 = \(3 \times 11,\) 39 = \(3 \times 13\) are composite. 25 is a multiple of 5.

In addition, what is left: 23, 29, 31, 37.

Primes: 23, 29, 31, 37.

Worksheet problems 11 and up

11 – Odd one out

Now, Test each number for a factor other than 1 and itself. 13 and 17 and 23 have no other factors. For 21, try 3: \(3 \times 7 = 21\).

So 21 has the factors 1, 3, 7 and 21, which is more than two.

Answer: 21 is not prime, because \(3 \times 7 = 21\).

12 – Divisibility by last digit

So, the last digit is 5.

(a) 5 is not 0, 2, 4, 6 or 8, so not divisible by 2.

(b) The last digit is 5, so divisible by 5.

Answer: (a) no, (b) yes, (c) no.

13 – Factor pairs of 36

\(1 \times 36\), \(2 \times 18\), \(3 \times 12\), \(4 \times 9\), \(6 \times 6\). The factor 6 is counted once.

Factor rainbow for 36.

Also, Factors: 1, 2, 3, 4, 6, 9, 12, 18, 36. Answer: 5 factor pairs, 9 factors.

Worksheet problem 14 and after

14 – Factors of 48

Then, Pairs: \(1 \times 48\), \(2 \times 24\), \(3 \times 16\), \(4 \times 12\), \(6 \times 8\). 5 and 7 do not divide 48.

Next, Factors: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 (10 factors).

15 – Sticker poster

In addition, Row lengths are the factors of 28. Pairs: \(1 \times 28\), \(2 \times 14\), \(4 \times 7\). (5 and 3 do not work.)

Three arrays, each with 28 stickers.

Now, Row lengths: 1, 2, 4, 7, 14, 28.

16 – Muffin boxes

So, the totals must be multiples of 6. \(6 \times 7 = 42\) and \(6 \times 9 = 54\). For 50: \(6 \times 8 = 48\), remainder 2. For 62: \(6 \times 10 = 60\), remainder 2.

Answer: 42 and 54.

17 – Team sizes

Also, Team sizes must be factors of 30: 1, 2, 3, 5, 6, 10, 15, 30.

Then, Keep sizes from 2 to 10: 2, 3, 5, 6, 10.

Answer: 2, 3, 5, 6 or 10 players per team.

Worksheet problem 18 and after

18 – Bus schedule

Next, add 15 minutes each time. After 8:45 come 9:00, 9:15 and 9:30.

9:30 AM is 90 minutes after 8:00, and \(15 \times 6 = 90\), so it is a multiple of 15.

Answer: 9:00, 9:15, 9:30; yes, a bus leaves at 9:30.

19 – Mystery prime

In addition, Primes between 40 and 50: 41, 43, 47 (42, 44, 46, 48, 50 are even, 45 is a multiple of 5, 49 = \(7 \times 7\)).

Now, Digit sums: 4 + 1 = 5, 4 + 3 = 7, 4 + 7 = 11.

Answer: 47.

20 – Ethan's claim

So, Try 3: \(3 \times 17 = 51\). So 51 has the factors 1, 3, 17 and 51.

Also, a prime number has only two factors, so 51 is composite.

Answer: No. 51 = \(3 \times 17,\) so it is composite.

Key facts behind this 4th grade factors and multiples worksheet answers

Key facts

Then, a factor pair multiplies to make the number, such as 3 and 8 for 24.
Also, a number has a limited list of factors but endless multiples.
Next, a prime number has exactly two factors; a composite number has more than two.
Then, the number 1 is neither prime nor composite, and 2 is the only even prime.
Last-digit patterns: 2 for even numbers, 5 for 0 or 5, 10 for 0.

Common mistakes with this 4th grade factors and multiples worksheet answers

In addition, Students match the number of factors but not the list. Instead, check each factor in your list against the key to find a missing one.
Now, Students skip the pair format in the key. Writing 1 times 36, 2 times 18, and so on makes it easy to see when a list is complete.
So, Students read problem 10 as a list of odd numbers. The key shows 23, 29, 31, and 37 are prime because each has only two factors.
Also, Students copy the reasoning for problem 20 without testing it. Also, check that 3 times 17 equals 51 on your own.

How to use these solutions

Then, count the factors in your list and compare with the key. Then, if the counts differ, test the numbers between to find the missed one.
Next, Redo each missed problem using pairs. Finally, a pair table makes it hard to overlook a factor. Repeat this habit on every problem for the best results.
In addition, Parents can ask the child to explain why 1 is not prime, using the idea that a prime has exactly two factors.

Now, Download the 4th grade factors and multiples worksheet answers as a PDF with the button below and keep it with your notes.

4th grade factors and multiples worksheet answers: frequently asked questions

How many factors does 36 have?

So, the number 36 has nine factors: 1, 2, 3, 4, 6, 9, 12, 18, and 36. Also, the factor pairs are 1 and 36, 2 and 18, 3 and 12, 4 and 9, and 6 and 6. The pair 6 and 6 counts the factor 6 only once.

How do I find the mystery prime in problem 19?

Also, list the primes between 40 and 50: 41, 43, and 47. Then find the one whose digits add to 11. For 47, 4 plus 7 is 11, so the mystery prime is 47. The other two sum to 5 and 7.

Which totals in problem 16 can be packed in boxes of 6?

Then, Only totals that are multiples of 6 work. Dividing 42 and 54 by 6 gives 7 and 9 with no remainder. The totals 50 and 62 leave remainders of 2, so they cannot be packed into full boxes of 6.

In addition, all Grade 4 chapters: Grade 4 math.

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