4th Grade Factors, Multiples, Prime and Composite Test Answer Key and Scoring Guide (PDF)

Q: What are the factor pairs of 40?

The factor pairs of 40 are 1 and 40, 2 and 20, 4 and 10, and 5 and 8. Also, that makes eight factors in all. Three and 6 do not divide 40 evenly, so they are not factors. Listing pairs in order helps you avoid missing any.

Q: How do you show a number is composite?

Find one factor pair other than 1 and the number. For 49, show that 7 times 7 equals 49. A single extra factor proves the number is composite, so you do not need to list all of its factors.

4th grade factors and multiples test answer key – Maths PDF

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This 4th grade factors and multiples test answer key 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 see how each point on the factors and multiples test was earned.

Topic: Factors, Multiples, Prime and Composite (4th grade)
Content: Worked solutions and a scoring guide for 9 questions
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 see how each point on the factors and multiples test was earned. Also, it gives complete solutions to all nine questions, with factor pairs written in order and the reasoning for prime and composite numbers explained in full sentences.

Then, question 6 explains why 1 is not prime, question 7 shows how to narrow down each riddle, and question 9 lists all valid desk arrangements. Add your points out of 20, then spend about 15 minutes redoing every question that lost credit. Write each factor list as pairs so you can see at a glance whether it is complete.

Use this answer key and scoring guide to grade the factors and multiples test. Each solution shows the work, and the scoring note explains how partial credit is awarded out of 20 points.

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

4th grade factors and multiples test answer key: worked solutions

1 – Factor pairs of 40 [2 pts]

\(1 \times 40\), \(2 \times 20\), \(4 \times 10\), \(5 \times 8\).

1 and 40, 2 and 20, 4 and 10, 5 and 8

Scoring: 2 points for all four pairs; 1 point for three pairs or for four pairs with one wrong extra pair; 0 points otherwise.

2 – Missing multiples [2 pts]

Next, count by 9: 9, 18, 27, 36, 45, 54, 63.

All multiples of 9 up to 63.

27 and 54

Scoring: 1 point for each correct missing number.

3 – Array and factors [2 pts]

7 rows of 3: \(7 \times 3 = 21\). Factor pairs: \(1 \times 21\), \(3 \times 7\).

Both arrays have 21 tiles.

\(7 \times 3\) = 21; factors 1, 3, 7, 21

Scoring: 1 point for a correct equation; 1 point for all four factors.

Question 4 and after

4 – Prime or composite [2 pts]

(a) 27 = \(3 \times 9\): composite. (b) 31 has only factors 1 and 31: prime. (c) 49 = \(7 \times 7\): composite. (d) 61 has only factors 1 and 61: prime.

(a) composite (b) prime (c) composite (d) prime

Scoring: 2 points for four correct; 1 point for two or three correct.

5 – Multiples of 9 [2 pts]

\(9 \times 7 = 63\), \(9 \times 8 = 72\), \(9 \times 11 = 99\). 85 and 91 are not (\(9 \times 9\) = 81, \(9 \times 10\) = 90, \(9 \times 11\) = 99).

63, 72, 99

Scoring: 2 points for all three and no extra numbers; 1 point if one is missing or one wrong number is included.

6 – Is 1 prime? [2 pts]

In addition, a prime number has exactly two factors. The number 1 has only one factor, 1 itself.

Mia is not correct. 1 has one factor, so it is not prime.

Scoring: 1 point for saying Mia is not correct; 1 point for a reason that mentions the number of factors.

Question 7 and after

7 – Number riddles [3 pts]

(a) \(8 \times 7 = 56\).

(b) The primes between 80 and 90 are 83 and 89. 8 + 3 = 11, 8 + 9 = 17.

(a) 56 (b) 83 (c) 15

Scoring: 1 point for each correct number.

8 – Divisibility [2 pts]

Now, the last digit is 5.

(a) no (b) yes (c) no

Scoring: 2 points for three correct; 1 point for two correct.

9 – Desk arrangements [3 pts]

(a) Factor pairs of 32: \(1 \times 32,\) \(2 \times 16,\) \(4 \times 8\). Rows and desks per row both at least 2: \(2 \times 16,\) \(4 \times 8,\) \(8 \times 4,\) \(16 \times 2\).

(b) 32 has more than two factors (1, 2, 4, 8, 16, 32).

Two of the arrangements.

(a) \(2 \times 16,\) \(4 \times 8,\) \(8 \times 4,\) \(16 \times 2\) (b) composite

Scoring: (a) 2 points for four arrangements, 1 point for two or three; (b) 1 point for composite with a reason.

Total score

Total

20 points

Key facts behind this 4th grade factors and multiples test answer key

Key facts

So, 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.
Also, 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 test answer key

Then, Students lose points because a factor list is missing one pair. Also, compare your list with the key and check numbers between the pairs.
Next, Students answer yes or no in question 6 without a reason. Instead, a complete answer says that 1 has only one factor.
In addition, Students solve riddles in question 7 by guessing. Also, use each clue to shrink the list, such as multiples of 8 between 50 and 60.
Now, Students ignore the rule about 2 rows in question 9. Instead, check each arrangement in your list against both conditions.

How to learn from your test

So, group missed questions into factors, multiples, and prime or composite. Practice the group with the most lost points first.
Also, rewrite each prime or composite answer with a factor pair as proof. Finally, a proof is the best way to show a number is composite.
Then, Teachers can ask students to explain one riddle answer to a partner, naming the clue that helped the most.

Next, Download the 4th grade factors and multiples test answer key as a PDF with the button below and keep it with your notes.

4th grade factors and multiples test answer key: frequently asked questions

What are the factor pairs of 40?

In addition, the factor pairs of 40 are 1 and 40, 2 and 20, 4 and 10, and 5 and 8. Also, that makes eight factors in all. Three and 6 do not divide 40 evenly, so they are not factors. Listing pairs in order helps you avoid missing any.

How do you show a number is composite?

Now, find one factor pair other than 1 and the number. For 49, show that 7 times 7 equals 49. A single extra factor proves the number is composite, so you do not need to list all of its factors.

Which numbers between 80 and 90 are prime?

So, Only 83 and 89 are prime between 80 and 90. The others are divisible by 2, 3, 5, or 7. For the riddle with digits that add to 11, neither 83 nor 89 works at first glance, so check the sums to find the match.

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