The idea in brief. Read the story for which way it goes. Sharing a fixed amount out into equal packets asks how big a number divides both counts, so the answer is a common factor, the greatest one. Something that repeats, or an equal number bought in different pack sizes, asks how far you count on before the two lists meet, so the answer is a common multiple, the first one. Write the two ladders or the two lists, and read the answer off them.
Lesson video, with the working
Factors and multiples in word problems
3 min 20 s
The film teaches 2 questions in turn. Each question shows first; its working is written as the film explains it.
A baker has fewer than 70 buns. She can pack all of them into boxes of 6 with none left over, or into boxes of 8 with none left over. What is the greatest number of buns she can have?
Common multiples of 6 and 8 that are less than 70: 24, 48
48 = 2 × 24
The greatest number of buns she can have is 48.
Ans: 48
Example 1
Boon Keat bought an equal number of pens and rulers. Pens are sold in packs of 6 and rulers are sold in packs of 9. What is the smallest possible number of packs of pens he bought?
Multiples of 6: 6, 12, (18), ...
Multiples of 9: 9, (18), ...
18 = 3 × 6 = 2 × 9
18 ÷ 6 = 3
The smallest possible number of packs of pens he bought was 3.
Ans: 3
How to solve it
If a total packs exactly in sixes and eights, it must be a multiple of both 6 and 8.
List the multiples below 70. The common multiples are 24 and 48.
Choose the greatest one below 70: 48 buns. Check that both pack sizes leave none over.
For equal totals of pens and rulers, list multiples of each pack size: 6, 12, 18 and 9, 18.
The smallest shared total is 18. Divide by the pen pack size: 18 divided by 6 is 3 packs of pens.
Read what the question asks: the number of items, or the number of packs.
Practice questions with worked solutions
Question 1 is free to try. The other 7 open in the free trial, each with its full working.
Question 1 of 8 · Basic · free to tryAt a bus interchange, Bus A leaves every 8 minutes and Bus B leaves every 12…At a bus interchange, Bus A…
At a bus interchange, Bus A leaves every 8 minutes and Bus B leaves every 12 minutes. Both buses leave together at 07 00. At what time do they next leave together?
How can I help my child choose a method for P4 factors word problems?
Your child applies common factors and common multiples to situations involving equal packets and repeating quantities.
What your child learns here
Your child applies common factors and common multiples to situations involving equal packets and repeating quantities. The MOE Primary 4 factor and multiple outcomes supply the arithmetic. Reading what the unknown represents is just as important: a number of identical packets is different from a total reached by two repeating sequences.
Identify whether the question divides existing amounts into equal groups or looks for a larger amount that can be made in different equal groups.
Use a common factor for the number of identical packets when each given supply must be distributed equally with nothing left over.
Use common multiples for matching repeat intervals, and distinguish the next shared occurrence from the starting event mentioned in the question.
Apply a maximum, minimum or stated range only after finding values that satisfy the factor or multiple conditions.
Label the final result as packets, items per packet, elapsed time or another requested quantity, since a valid intermediate number may answer a different question.
Does the answer make sense?
For a proposed number of identical packets, divide each original supply by that packet count. Both results must be whole numbers, and multiplying each packet's contents by the number of packets must recover the corresponding original supply without leftovers.
How to practise these questions
Basic questions find the next shared departure time for two repeating services or the greatest number of identical bags. Intermediate practice includes divisibility after a small change, events with different starting times, equal ribbon lengths and numbers satisfying two remainder conditions. Challenge questions combine equal sharing with a shortage, or connect a factor and a multiple through a total. Ask your child to describe the unknown before beginning a list. For events with different starting times, list the actual occurrence times from each stated start; a shared interval alone does not settle their first meeting. For a number clue, test the candidate in its original and changed forms, then answer the final quantity requested.
Questions parents ask
How does my child know whether a story needs factors or multiples? Ask what is fixed and what must be found. Splitting fixed supplies equally suggests factors of those supplies. Finding a shared total or repeat time suggests multiples of the group sizes or intervals. Your child can test that interpretation against the units of the requested answer.
Does the greatest number of packets give the most items per packet? No. When the same supplies are shared among more identical packets, each packet contains fewer items. Your child should keep the packet count separate from each packet's contents. The words greatest and smallest refer to the particular quantity named in the question.
Should the starting event count when finding the next meeting? A request for the next time two events occur together means a later occurrence. The shared start establishes the beginning of the interval. Your child first finds the positive elapsed time and then, if needed, adds it to the stated starting time.
