(a) Express 72 as a product of its prime factors.

(b) Find the smallest positive integer value n for which 72n is a cube number.

Consider the given numbers:
0.4, 23, 23, 1, 2
Write down a number that is:
(a) Prime

(b) Irrational

(c) A square number

(a)(i) Express 130 as a product of its prime factors.

(a)(ii) Find the smallest positive integer value n for which 130n is a multiple of 35.

(b) Find the highest common factor (HCF) of 48 and 84.

24=2×2×2×3
(a) Find the smallest integer value of t for which 24 t 3 is an integer.

(b) The number 240 can be expressed as a product of a cube number, j which is greater than 1, a composite number, k and a multiple of 5, l. Find the values of j, k and l.

(a) Write 520 as a product of its prime factors.

(b) It is given that 1260=22×32×5×7. Find the highest common factor of 1260 and 520.

Consider the numbers:
−π11, 8.215, 2337, 9, 643
Write the number which is:
(a) irrational

(b) prime

(c) a perfect square

From the list of numbers: 2.4, 5, 8%, 15, 16
Write:
(a) A composite number

(b) An integer

(c) An irrational number

From the following list of numbers:
3 π 2 32 35 121
Write:
(a) a multiple of 7

(b) a factor of 8

(c) a prime number

(d) a square number

(e) an irrational number

(a) Express 56 as the product of its prime factors.

(b) The number P expressed as the product of its prime factors is 2×3×7. Find the HCF of 56 and P.

(a) Write 126 as a product of its prime factors.

(b) Find the difference between the fifth prime number and the fourth composite number.

(c) Show that 2.12 is rational.

In 1950, the population of Switzerland was 4 714 900. In 2000, the population was 7 087 000.

(a) Work out the percentage increase in the population from 1950 to 2000.

(b) (i) Write the 1950 population correct to 3 significant figures.

(ii) Write the 2000 population in standard form.

Write the numbers ${0.5}^2$, $\sqrt{0.5}$, ${0.5}^3$ in order with smallest first.

Work out $\frac{5}{6}$ − $(\frac{1}{2}\times 1\frac{1}{2})$.
Write down all the steps of your working.

Calculate $\frac{5^2}{2^5}$.
(a) Giving your answer as a fraction,

(b) Giving your answer as a decimal.

Write down the next two prime numbers after 47.

Write $2^8$ × $8^2$ × $4^{-2}$ in the form $2^n$.

Show that $1\frac{5}{9}$ ÷ $1\frac{7}{9}$ = $\frac{7}{8}$.
Write down all the steps in your working.

For this question, 1 < x < 2.
Write the following in order of size, smallest first.
$\frac{5}{x}$, $5x$, $\frac{x}{5}$, $x-5$

$1\frac{1}{2}$ + $\frac{1}{3}$ + $\frac{1}{4}$ = $\frac{p}{12}$.
Work out the value of p. Show all your working.

Without using a calculator, work out $\frac{6}{7}$ ÷ $1\frac{2}{2}$.
Write down all the steps in your working.