GCSE Foundation — Number
25% of a GCSE Foundation entry is number, spread across all three papers rather than gathered into one. The DfE lists 16 content statements for number at this tier, and the question bank is organised by them rather than by chapter headings, so you can see exactly which one you are weak on. Expect ordering numbers and inequality symbols, the four operations and place value, inverse operations and priority of operations, factors, multiples, primes, HCF and LCM, systematic listing and the product rule for counting and powers and roots. Everything on this page is Foundation content, which means a Higher student needs it too — Higher is Foundation plus more, not instead of. The assessment objectives split 50% AO1 against 50% AO2 and AO3 combined, which is why so many questions ask you to explain or to justify rather than simply to calculate. Most of this area is natural Paper 1 material, so practise it without a calculator before you practise it with one.
- N1 — Ordering numbers and inequality symbols
- N2 — The four operations and place value
- N3 — Inverse operations and priority of operations
- N4 — Factors, multiples, primes, HCF and LCM
- N5 — Systematic listing and the product rule for counting
- N6 — Powers and roots
- N7 — Calculating with roots and indices
- N8 — Exact calculation: fractions, surds and π
- N9 — Standard form
- N10 — Fractions and decimals, including recurring decimals
- …and 6 more number statements at this tier
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Number at GCSE Foundation: the 16 DfE statements
Every question on this site is filed against one of these statements. Pick one to practise it on its own.
Sample number questions for GCSE Foundation
- Amelia eats 5/8 of a bar of chocolate and Oliver eats 3/4 of an identical bar. Write both amounts as eighths and write down the greater of the two fractions.(a)7/8(b)1/8(c)6/8(d)5/8
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6/8 — Method: two fractions can only be compared directly when they share a denominator, so rewrite 3/4 in eighths and then compare the numerators. Working: 5/8 is already in eighths, and 3/4 = (3 × 2)/(4 × 2) = 6/8. Comparing the numerators, 6 > 5, so Oliver eats the larger share. Answer: 6/8. The distractors: 5/8 comes from skipping the conversion altogether and assuming that a bar cut into eighths must give the bigger share because it has more pieces; once both shares are written over the same denominator, 5 eighths is one eighth less than 6 eighths. 1/8 comes from working out how much more Oliver eats, 6/8 − 5/8, instead of writing down the greater of the two shares. 7/8 comes from adding 4 to the numerator and 4 to the denominator of 3/4 instead of multiplying both by 2. - Which of these numbers lies between −4 and −1 on a number line?(a)−5(b)2(c)0(d)−2
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−2 — Method: place the two end values on a number line and list the integers that sit strictly between them. Working: reading from left to right the integers run −4, −3, −2, −1, so the values strictly between the ends are −3 and −2. Only one of those is offered. Answer: −2. The distractors: −5 comes from ordering negatives by the size of their digits, which wrongly places −5 to the right of −4; 0 comes from carrying on past −1 instead of stopping at it; 2 comes from ignoring the minus signs and choosing a number between 1 and 4. - Write these numbers in order, starting with the smallest: 3, −1, 0, −5(a)3, 0, −1, −5(b)−1, −5, 0, 3(c)0, −1, −5, 3(d)−5, −1, 0, 3
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−5, −1, 0, 3 — Method: order the numbers by their position on a number line, smallest (furthest left) first. Working: both −5 and −1 lie to the left of 0, and 3 lies to the right of 0. Of the two negatives, −5 is 5 units from zero and −1 is 1 unit from zero, so −5 is further left. Answer: −5, −1, 0, 3. The distractors: 3, 0, −1, −5 is the correct order written the wrong way round, starting with the largest; −1, −5, 0, 3 comes from ordering the two negatives by the size of their digits, so that −1 is treated as the smaller; 0, −1, −5, 3 comes from believing that zero is the smallest number there is and then listing the negatives by their digits. - On one night in Manchester the temperature at 3 am was 8 °C below zero and at 9 am it was 3 °C below zero. Write down the warmer of the two readings.(a)−3 °C(b)3 °C(c)5 °C(d)−8 °C
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−3 °C — Method: write each reading as a signed temperature, then choose the one further to the right on a number line. Working: 8 °C below zero is −8 °C and 3 °C below zero is −3 °C. On a number line −3 lies to the right of −8, so it is the warmer reading. Answer: −3 °C. The distractors: −8 °C comes from ordering negatives by the size of their digits, treating −8 as the larger number; 3 °C has the right size but the sign dropped, and a reading of 3 °C is above zero rather than below it; 5 °C comes from working out the difference between the two readings instead of choosing one of them. - On a number line, point A is at −1. Point B is 4 units from point A. Write down the two possible positions of point B.(a)5 or −3(b)4 or −4(c)3 or −5(d)3 only
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3 or −5 — Method: a point a fixed distance from another can lie on either side of it, so move the given distance in each direction from the starting point. Working: moving 4 units to the right gives −1 + 4 = 3, and moving 4 units to the left gives −1 − 4 = −5. Answer: 3 or −5. The distractors: 5 or −3 comes from starting at 1 instead of −1, giving 1 + 4 and 1 − 4; 3 only comes from moving to the right and forgetting that the point could lie to the left as well; 4 or −4 comes from measuring the distance from zero instead of from point A, which just repeats the given distance.
Frequently asked questions
How much of the GCSE Foundation paper is number?
25% of the total marks, and the three papers each carry an equal share of the qualification, so it is spread across all of them rather than concentrated in one.
How many topics are there in number at GCSE Foundation?
16 DfE content statements, coded N1 to N16 within this area. Every question in the bank is tagged to one of them.
Is any number content on this page Higher only?
No. Foundation pages only show statements a Foundation entry may be asked. The Higher-only number material is on the GCSE Higher page for this area.
Can I use a calculator for number questions?
Paper 1 is non-calculator; Papers 2 and 3 allow one. Of the 16 statements in this area, 10 are naturally non-calculator and 1 naturally calculator, with the rest workable either way — so practise both.
What kind of marks does number carry?
The GCSE Foundation split is 50% AO1 (use and apply standard techniques), 25% AO2 (reason, interpret and communicate) and 25% AO3 (solve problems in and out of context). Questions in this area are set across all three.
Are these past paper questions?
No. Every question at /gcse-foundation is original, written to the DfE content statements and checked before it is published. We do not host past papers or mark schemes.
Do I need an account?
No — you can start practising straight away. Progress is saved automatically in your browser.
Is it free?
Yes. The questions, worked answers and printable worksheets are all free, with no adverts.
Tips for number at GCSE Foundation
- To write a number as a product of its prime factors, divide repeatedly by the smallest prime that goes in (2, 3, 5, 7 …) until you reach 1, then write the answer as a product of powers of primes.
- For the lowest common multiple (LCM) of two numbers, write each as a product of primes and take every prime at the highest power that appears. For the highest common factor (HCF), take only the shared primes, each at the lower power.
- A prime number has exactly two factors, 1 and itself. 1 is not prime, and 2 is the only even prime.
- Divisibility tests speed up factorising: a number is divisible by 2 if it is even, by 3 if its digit sum is divisible by 3, and by 5 if it ends in 0 or 5.
- Standard form writes a number as a × 10ⁿ with 1 ≤ a < 10. It is the tool for very large and very small numbers, and it turns up on the calculator papers as well as Paper 1.
Common mistakes (and how to avoid them)
- Including 1 as a prime factor — 1 is not prime and never appears in a prime factorisation.
- Stopping the factor tree at a composite number, such as writing 12 = 4 × 3 without splitting the 4 into 2 × 2.
- Taking the higher power for the HCF (or the lower power for the LCM) — the rule is exactly the other way round.
- Writing 35 × 10⁴ as standard form. The first number must be between 1 and 10, so the correct form is 3.5 × 10⁵.
Worked examples
- 60 is even, so divide by 2: 60 = 2 × 30.
- 30 is even, so divide by 2 again: 30 = 2 × 15.
- 15 divides by 3: 15 = 3 × 5, and 5 is prime.
- Collect the factors: 60 = 2 × 2 × 3 × 5 = 2² × 3 × 5.
- Factorise: 12 = 2² × 3 and 18 = 2 × 3². For the LCM take each prime at its highest power: 2² × 3² = 4 × 9 = 36.
- Factorise: 24 = 2³ × 3 and 36 = 2² × 3². For the HCF take the shared primes at the lower power: 2² × 3 = 4 × 3 = 12.
- Multiplying powers of the same base adds the indices: 2⁻³ × 2⁵ = 2² = 4.
- 350 000 = 3.5 × 100 000 = 3.5 × 10⁵, and 3.5 lies between 1 and 10 as required.
Number is a quarter of the Foundation paper, and most of it is method rather than mystery: factor trees, HCF and LCM, index laws and standard form all follow short rules that reward careful practice. Prime factorisation is the identity card of every whole number — each one has exactly one — and it is the tool you reach for when adding fractions or simplifying ratios. Keep the HCF and LCM rules the right way round, work Paper 1 questions without a calculator, and check each answer by multiplying back.
More GCSE Foundation maths:
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