4th Grade Factors, Multiples, Prime and Composite Test Solutions and Scoring (PDF)

4th Grade math test solutions: Factors, Multiples, Prime and Composite – Maths PDF

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

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

Factors multiples test answers: worked solutions

Question 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.

Question 2 – Missing multiples [2 pts]

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.

Question 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 – 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.

Question 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.

Question 6 – Is 1 prime? [2 pts]

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 – 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.

Question 8 – Divisibility [2 pts]

The last digit is 5.

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

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

Question 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 factors multiples test answers

Key facts

A factor pair multiplies to make the number, such as 3 and 8 for 24.
A number has a limited list of factors but endless multiples.
A prime number has exactly two factors; a composite number has more than two.
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.

How to use this factors multiples test answers

Score your test with the point values shown for each question. Then read the worked solution of every question where you lost points and note the method to review.

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