The Fundamental Theorem of Arithmetic, Quiz

What is the prime factorisation of

1260

?

A

2^2 \times 3^2 \times 5 \times 7

B

2 \times 3^2 \times 7 \times 10

C

2^2 \times 3 \times 5 \times 21

D

2^3 \times 3^2 \times 7

Which number has the prime factorisation

2^3 \times 3^2 \times 5

?

A

180

B

720

C

270

D

360

The Fundamental Theorem of Arithmetic says the prime factorisation of a composite number is unique apart from what?

A The largest prime used

B The order of the factors

C The number of factors

D The powers of

2

Write

3600

as a product of prime powers.

A

2^4 \times 3^2 \times 5^2

B

2^3 \times 3^2 \times 5^2

C

2^4 \times 3 \times 5^2

D

2^4 \times 3^2 \times 5

Why can

4^n

never end in the digit

0

for any natural number

n

?

A Because

4^n

is always a perfect square

B Because

4

is an even number

C Its only prime factor is

2

, so

5

never divides it

D Because

4^n

is less than

10^n

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