CTJan27 Online Year 5 - Factors and Prime Numbers

1

How many factors does the number $96$ have?

8 10 12 14

2

Which of the following numbers is a factor of $135$ but not a factor of $90$?

5 15 27 45

3

A number has factors $1, 2, 4, 8, 16, 32$. What is the largest factor of this number that is also a factor of $24$?

4 8 16 32

4

If $12$ is a factor of $A$, and $A$ is a factor of $144$, which of the following MUST be true?

$A$ must be a prime number. $144$ is a multiple of $12$. $12$ must be equal to $A$. $A$ must have an odd number of factors.

5

Which number below has exactly $3$ factors?

12 25 16 27

6

Find the set of common factors for $36$ and $54$.

$\{1, 2, 3, 6, 9, 18\}$ $\{1, 2, 4, 6, 9, 12\}$ $\{1, 2, 3, 6, 9\}$ $\{1, 2, 3, 6, 18, 27\}$

7

Which of the following numbers has the most factors?

72 88 92 98

8

What is the Greatest Common Factor (GCF) of $75$ and $105$?

5 15 25 35

9

The factors of a number include $1, 2, 4, 5, 8, 10, 20$. If this number is greater than $40$, what is the smallest possible value for this number?

60 80 100 40

10

If the pair of factors for $120$ is $(8, X)$, what is the next factor pair for $120$ after $8$ in ascending order?

$(10, 12)$ $(9, 13.33...)$ $(12, 10)$ $(10, 15)$

11

Which number has only prime numbers as its factors (excluding $1$)?

24 30 35 49

12

Which list correctly shows all the factors of $84$?

$\{1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84\}$ $\{1, 2, 3, 4, 6, 7, 12, 21, 28, 42, 84\}$ $\{1, 2, 3, 4, 6, 8, 12, 14, 21, 28, 42, 84\}$ $\{1, 2, 3, 4, 6, 7, 12, 14, 24, 28, 42, 84\}$

13

How many composite factors does $30$ have?

4 5 6 8

14

Identify all the prime factors of $105$.

$\{3, 5, 7\}$ $\{1, 3, 5, 7\}$ $\{5, 7, 15\}$ $\{3, 5, 7, 105\}$

15

Which of the following statements is true?

All factors of a number are always less than half the number. The GCF of any two prime numbers is always $1$. Every factor of $20$ is also a factor of $10$. Every multiple of $8$ has $4$ factors.

16

If $A$ is a number such that $4$ and $9$ are both factors of $A$, what is the smallest possible value for $A$?

13 36 72 108

17

What is the product of all the factors of $10$?

10 30 100 250

18

Find the sum of all factors of $16$.

16 24 31 40

19

Which list contains only the composite factors of $48$?

$\{4, 6, 8, 12, 16, 24, 48\}$ $\{4, 6, 8, 12, 24\}$ $\{1, 4, 6, 8, 12, 24\}$ $\{4, 6, 8, 12, 16, 24\}$

20

If a number $N$ is a perfect square, which property must be true about its factors?

It must have exactly $4$ factors. It must have an even number of factors. It must have an odd number of factors. It must have fewer than $6$ factors.

21

Which statement correctly describes the number $1$?

It is a prime number because it only has one factor. It is a composite number because it is the start of all numbers. It is neither a prime nor a composite number. It is a prime number because it is an odd number.

22

Which of the following numbers is a prime number?

$87$ $91$ $97$ $111$

23

What is the sum of all prime numbers strictly between $10$ and $20$?

$50$ $60$ $61$ $65$

24

The number $78$ is written as the product of three distinct prime numbers. Which set shows these three prime numbers?

$\{2, 3, 13\}$ $\{2, 5, 7\}$ $\{3, 5, 11\}$ $\{2, 3, 11\}$

25

If $P$ is the only even prime number, what is the value of $P^3 - 1$?

$3$ $5$ $7$ $9$

26

Which of the following numbers has exactly four factors?

$16$ $25$ $33$ $49$

27

What is the greatest difference between two consecutive prime numbers less than $50$?

$4$ $6$ $8$ $10$

28

A number $N$ has a prime factorization of $2^2 \times 3 \times 5$. What is the smallest composite factor of $N$?

$2$ $3$ $4$ $6$

29

Which pair of numbers are classified as 'twin primes'?

$(11, 13)$ $(13, 17)$ $(15, 17)$ $(21, 23)$

30

How many prime numbers are there between $60$ and $80$?

$4$ $5$ $6$ $7$

31

Identify the number in the set $\{31, 47, 59, 63\}$ that is NOT a prime number.

$31$ $47$ $59$ $63$

32

Which number is the $10^{th}$ smallest prime number?

$23$ $27$ $29$ $31$

33

If $P_1$ and $P_2$ are two distinct prime numbers, which of the following expressions \textbf{must} result in a composite number?

$P_1 + P_2$ $P_1 - P_2$ $P_1 \times P_2$ $P_1^2 + 1$

34

If $3 \times 5 \times X = 165$, and $X$ is a prime number, what is the value of $X$?

$7$ $11$ $13$ $17$

35

A composite number $C$ is less than $50$. If the smallest prime factor of $C$ is $5$, what is the smallest possible value of $C$?

$10$ $15$ $25$ $35$

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