The idea in brief. A factor never comes alone. Climb the ladder from 1, writing the number as a product on every rung, and stop when the pairs turn round; every factor is now on the ladder. A common factor is a number that stands on both ladders, so both ladders are written before anything is circled.
Lesson video, with the working
Common factors, and the greatest of them
3 min 57 s
The film teaches 2 questions in turn. Each question shows first; its working is written as the film explains it.
Question 1 of 14 · Basic · free to tryList all the factors of 24.List all the factors of 24.
List all the factors of 24.
Show the working and the answer
Working
24 = 1 × 24
= 2 × 12
= 3 × 8
= 4 × 6
The factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24.
Answer: 1, 2, 3, 4, 6, 8, 12 and 24
For parents
How can I help my child find P4 common factors systematically?
Your child learns how factors relate to multiplication and division, then finds factors shared by two numbers.
What your child learns here
Your child learns how factors relate to multiplication and division, then finds factors shared by two numbers. The MOE Primary 4 outcomes include testing whether a 1-digit number is a factor of a number within 100 and finding common factors. Organising factor pairs helps your child explain why the list is complete.
Recognise that a factor divides a whole number exactly, leaving no remainder, and connect that division to a corresponding multiplication fact.
Find factors in pairs whose product is the given number, including one paired with the number itself.
List the factors of each number separately before identifying the entries that occur in both lists, keeping factors distinct from multiples.
Record a repeated member of a factor pair only once in the final list, as happens when the number is a square number.
Use the wording of the question to decide whether to give every common factor, one possible factor or the greatest factor shared.
Combine clues about known factors and the total number of factors to identify an unknown number, checking its complete factor list.
Does the answer make sense?
When clues give some factors and the total number of factors, your child can list every factor of the proposed answer in pairs. The list must include all the named factors and contain exactly the required number of distinct entries, counting a repeated factor only once.
How to practise these questions
Basic questions list factors or test whether a number is a factor. Intermediate practice completes factor lists, finds shared factors and checks factor and multiple conditions. The Challenge questions recover a number from known factors and a specified total number of factors. Your child therefore needs to find a candidate and verify its entire factor list, rather than stop when the named factors divide it. Begin the attempt by listing the clues separately. Use multiplication facts and exact division to construct factor pairs, then count each distinct factor once. If the candidate has too many or too few factors, revisit the candidate rather than changing the required count. Reviewing the solution should clarify how both kinds of clue restrict the answer. The multiple-choice Basic questions ask which number is a common factor of two numbers, or which statement about the factors of the numbers on three cards is true.
Questions parents ask
What makes a factor common to two numbers? It must be a factor of each number independently. Being a factor of just one number does not meet the condition. Have your child test the same candidate with two divisions, then explain that both remainders are zero before putting it in the common list.
Why are factor pairs useful for my child? Every exact division reveals two factors at once: the divisor and the quotient. Writing them as a pair makes it easier to account for both small and large factors. Your child can then arrange the factors in order and see whether any have been recorded twice.
Must my child use prime factorisation in Primary 4? The stated Primary 4 outcomes do not require prime factorisation. Multiplication facts, factor pairs and exact division are enough for the factor work described here. Encourage a clear, organised list and a division check before introducing a more advanced method that your child may not need.
