7.1 Positive Integers

Fill in the missing digit: 3_7 + 285 = 632. Which digit is missing and in which place? Justify your answer.

Round 2364 to the nearest hundred and name the digit that decided the rounding. Justify.

If 523 − ?? = 355, what is the missing number? Show how you would check your answer.

Without fully calculating, decide: is 34 × 6 closer to 180 or 210? Justify.

Is 4728 divisible by 4? Use short division to check. Show your working and state whether there is a remainder.

Is 84 divisible by 4? Use short division to find out. Show enough working to be sure.

Find ONE factor of 36 (other than 1 and 36) and justify that it is a factor.

Which is the smallest multiple of 7 that is greater than 40? Justify.

Is 91 a prime number? Justify with at least one trial division.

Without working out the exact value of $9^2$, decide: is $9^2$ greater or less than 100? Justify.

Round 3467 to the nearest ten.

Calculate 2847 + 1965.

Calculate 5023 − 2648.

Calculate 1848 ÷ 7.

Work out 5 + 3 × 8 using the correct order of operations.

Find the HCF of 24 and 36.

Find the LCM of 6 and 8.

What is 4 cubed? Write ${4}^3$.

Write 28 as a product of prime factors.

Each notebook costs £3. How much do 14 notebooks cost?

Work out $(5 + 7) \times 4 - 18 \div 3$.

Find the HCF of 12, 18 and 30.

Express 84 as a product of prime factors in index form.

Work out $\sqrt[3]{{216}}$.

Without calculating exactly, decide which is larger: 23 × 24 or 22 × 25. Explain your reasoning.

Calculate ${4}^2 \times 3$.

Find a number that is both a multiple of 6 and a factor of 60.

Estimate 47 × 18 by rounding each number to 1 significant figure.

Apples cost 35p each. Oranges cost 50p each. Sam buys 4 apples and 3 oranges and pays with a £5 note. How much change does he receive?

Work out $(7^2 - 4) \div 5 + 6$.

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 180.

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 = 6 and LCM = 60. Find all possible pairs of numbers.

Is 91 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 7. Find all such numbers.

Two whole numbers $a$ and $b$ satisfy $a \times b = 56$ and $a + b = 15$, with $a > b$. Find $a$ and $b$.

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

Work out $(9^2 - (2 + 3)^2) \div ((9 - 2 - 3) \times 4)$.

A school raises £1800 for a trip. Transport costs £480. The remaining money is split equally among 24 students. Each student pays £15 on top of their share. How much does each student have in total to spend?