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What it is
A multiple is a number you reach by skip counting. Count in 3s and you get 3, 6, 9, 12, the multiples of 3. A common multiple sits in two skip-counting lists at once.
Why it works
Skip counting in 3s always lands on 3 times a whole number, so every stop is a multiple of 3. Two lists first meet at their lowest common multiple, then meet again each time that same gap repeats.
Why it matters
Multiples help you arrange things in equal groups and spot when two things line up, like two lights blinking or two buses arriving together.
A few examples
Multiples of 5 are 5, 10, 15, 20. 15 is a common multiple of 3 and 5. The smallest common one, 15, is the lowest common multiple.
What it is
A prime number has exactly two factors, 1 and itself. A composite number has more than two factors.
Why it works
If a number's dots can be laid out as a full rectangle with more than one row, those rows and columns are factors, so it is composite. If the dots only ever make a single line, the only factors are 1 and the number, so it is prime.
Why it matters
Primes are the building blocks of all numbers. Every other number is made by multiplying primes together, so knowing them helps you understand every number.
A few examples
7 is prime (only 1 and 7). 12 is composite (1, 2, 3, 4, 6, 12). The number 1 is neither prime nor composite.
What it is
A factor divides a number exactly, with nothing left over. The factors of 12 are 1, 2, 3, 4, 6 and 12.
Why it works
Factors always come in pairs that multiply to the number, like 3 and 4 make 12, or 2 and 6 make 12. That is why you can hunt for factors by looking for pairs.
Why it matters
Factors show every equal group you can split a number into, which helps with sharing fairly and with simplifying fractions.
A few examples
6 is a factor of 18. Factors of 10 are 1, 2, 5, 10. The common factors of 12 and 18 are 1, 2, 3 and 6.
What it is
Prime factorisation means breaking a number into a product of only prime numbers. It is like the number's own secret recipe.
Why it works
Keep splitting a composite number into two factors, then split those, and you can only stop when every piece is prime, because a prime cannot be split further. However you split, you reach the same primes, so each number has just one recipe.
Why it matters
Every number has exactly one prime recipe. This helps you compare numbers, simplify fractions, and find the LCM and HCF later on.
A few examples
12 = 2 × 2 × 3. 30 = 2 × 3 × 5. 24 = 2 × 2 × 2 × 3.
What it is
Divisibility rules are quick tests that use the digits of a number to check if another number divides it, with no long division needed.
Why it works
Every ten is nine plus one, and nine is a multiple of 3. So when you break a number into its tens and ones, the tens always carry a multiple of 3, and only the leftover digits decide. That is why adding the digits works for 3 and for 9.
Why it matters
They save you time and help you spot factors fast, which is handy in every part of maths.
A few examples
Ends in an even digit → divides by 2. Ends in 0 or 5 → divides by 5. Digit sum a multiple of 3 → divides by 3, so 72 works because 7 + 2 = 9.
What it is
Two numbers are co-prime when their only common factor is 1, even if each one on its own is not prime.
Why it works
If two numbers shared a factor bigger than 1, you could divide both by it. Co-prime means no such number exists except 1, so the pair cannot be simplified together, which is exactly why a fraction with a co-prime top and bottom is already in simplest form.
Why it matters
Co-prime pairs are used in locks and gears, and they tell you when a fraction is already in its simplest form.
A few examples
8 and 9 are co-prime. 6 and 35 are co-prime. But 6 and 9 are not, because they share the factor 3.
Have a go on paper first, then tap to see the clear steps.
Q1. Find the common multiples of 3 and 4 up to 24.
Q2. Is 738 divisible by 3?
Q3. Write 36 as a product of prime numbers.
Q4. List all the factors of 24.
Q5. Are 14 and 15 co-prime?
Q6. Find the lowest common multiple (LCM) of 4 and 6.