Real Numbers Practice 1: Prime Factorisation and FTA

Section A: Concept Check

Question 1mcq

Which of these numbers is neither prime nor composite?

A.1

B.2

C.9

D.11

Question 2mcq

A student says

91

is prime because it is odd. What is the best response?

A.

91

is prime because all odd numbers are prime.

B.

91

is composite because

91=7\timesimes13

.

C.

91

is prime because it is not divisible by

2

.

D.

91

is neither prime nor composite.

Question 3mcq

What is the prime factorisation of

360

?

A.

2^2\timesimes3^2\timesimes5

B.

2^3\timesimes3\timesimes5^2

C.

2^3\timesimes3^2\timesimes5

D.

2\timesimes3^2\timesimes5

Question 4mcq

A shopkeeper packs

420

pencils into equal bundles using prime-factor groups. Which expression correctly shows

420

as a product of primes?

A.

2\timesimes3^2\timesimes5\timesimes7

B.

2^2\timesimes3\timesimes7

C.

2\timesimes3\timesimes5^2\timesimes7

D.

2^2\timesimes3\timesimes5\timesimes7

Question 5mcq

Which statement best represents the Fundamental Theorem of Arithmetic?

A.Every number has exactly two factors.

B.Every integer greater than

1

has a unique prime factorisation, apart from the order of factors.

C.Every composite number is divisible by

10

.

D.Every odd number is prime.

Section B: Reason and Apply

Question 6mcq

Two students write

84=2\timesimes2\timesimes3\timesimes7

and

84=7\timesimes3\timesimes2\timesimes2

. What does this show about FTA?

A.The number

84

has two different prime factorisations.

B.FTA fails for even numbers.

C.

84

is prime because it has prime factors.

D.The prime factorisation is the same; only the order has changed.

Question 7mcq

Given

A=2^3\timesimes3^2\timesimes5

and

B=2^2\timesimes3^3

, which number is divisible by

45

?

A.

A

only

B.

A

and

B

both

C.

B

only

D.Neither

A

nor

B

Question 8mcq

Which number is larger:

2^4\timesimes3^2

or

2^3\timesimes3^3

?

A.

2^4\timesimes3^2

B.They are equal

C.

2^3\timesimes3^3

D.Cannot be compared without expanding

Question 9mcq

A factory packs identical bolts in boxes of

72

. Which prime-factor form is most useful to compare with box sizes

8

,

9

, and

12

?

A.

72=2\timesimes36

B.

72=6\timesimes12

C.

72=70+2

D.

72=2^3\timesimes3^2

Question 10mcq

A rectangular floor has

96

identical tiles. To explain all possible equal row-column arrangements, which idea is most useful?

A.Prime factorisation helps generate factor pairs of

96

.

B.Only checking divisibility by

2

is enough.

C.Prime numbers cannot help with arrangements.

D.The arrangement is fixed as

1\timesimes96

only.