7.1 Positive Integers

Fill in the missing digit: 4_3 + 378 = 841. Which digit is missing and in which place? Justify your answer.

Round 7819 to the nearest thousand and name the digit that decided the rounding. Justify.

If 741 − ?? = 448, what is the missing number? Show how you would check your answer.

Without fully calculating, decide: is 47 × 8 closer to 350 or 400? Justify.

Is 5913 divisible by 3? Use short division to check. Show your working and state whether there is a remainder.

Is 135 divisible by 9? Use short division to find out. Show enough working to be sure.

Find ONE factor of 48 (other than 1 and 48) and justify that it is a factor.

Which is the smallest multiple of 9 that is greater than 50? Justify.

Is 43 a prime number? Justify with at least one trial division.

Without working out the exact value of $7^2$, decide: is $7^2$ greater or less than 50? Justify.

Round 8352 to the nearest hundred.

Calculate 5384 + 2769.

Calculate 7104 − 3857.

Calculate 2484 ÷ 9.

Work out 12 + 4 × 7 using the correct order of operations.

Find the HCF of 30 and 42.

Find the LCM of 4 and 10.

What is 5 cubed? Write ${5}^3$.

Write 30 as a product of prime factors.

Each notebook costs £7. How much do 12 notebooks cost?

Work out $(8 + 6) \times 3 - 20 \div 4$.

Find the HCF of 20, 28 and 36.

Express 120 as a product of prime factors in index form.

Work out $\sqrt[3]{{343}}$.

Without calculating exactly, decide which is larger: 31 × 34 or 32 × 33. Explain your reasoning.

Calculate ${6}^2 \times 5$.

Find a number that is both a multiple of 4 and a factor of 48.

Estimate 63 × 29 by rounding each number to 1 significant figure.

Apples cost 45p each. Oranges cost 60p each. Sam buys 3 apples and 4 oranges and pays with a £5 note. How much change does he receive?

Work out $(8^2 - 4) \div 6 + 3$.

Given $p = 2^3 \times 3 \times 5$ and $q = 2^2 \times 3^2 \times 7$, find the HCF and LCM of $p$ and $q$.

Find the largest prime factor of 156.

In the multiplication below, each letter stands for a different digit. Find A and B. $$\overline{4A} \times 3 = \overline{14B}$$

Two whole numbers have HCF = 4 and LCM = 48. Find all possible pairs of numbers.

Is 97 a prime number? Show your reasoning.

A number satisfies all of these: it is two-digit, it is prime, and the sum of its digits is 8. Find all such numbers.

Two whole numbers $a$ and $b$ satisfy $a \times b = 60$ and $a + b = 17$, with $a > b$. Find $a$ and $b$.

Explain why the product of any two consecutive even numbers is always divisible by 8.

Work out $(10^2 - (3 + 2)^2) \div ((10 - 3 - 2) \times 5)$.

A school raises £2200 for a trip. Transport costs £640. The remaining money is split equally among 40 students. Each student pays £12 on top of their share. How much does each student have in total to spend?