Multiples, factors and clever counting
Find multiples on the hundred chart, pack factors into rectangles, and learn three tricks that make sums easier: swap, group and break up. Read one step, play with it, then tap “I understand this”.
Multiples
The multiples of a number are the answers when you multiply it by 1, 2, 3, 4 … The multiples of 3 are 3, 6, 9, 12, 15 … It is just the 3 times table!
The hundred chart
Choose a number and look at the pattern of its multiples.
Multiples of 2 are even numbers. Multiples of 5 end in 0 or 5. Multiples of 10 end in 0.
Factors
A factor divides exactly into a number, with no remainder. Pack the number’s dots into a rectangle: every rectangle gives two factors. 12 = 3 × 4, so 3 and 4 are factors of 12.
Pack into rectangles
Choose a number and see in how many ways you can pack it.
Factors are small (they divide into the number); multiples are big (they come from the table). 3 is a factor of 12, and 12 is a multiple of 3.
You can always pack all the dots in one long row: 1 row of 12 is 12. That is why 1 and the number itself are always factors.
Swap and group
- Swap: with plus and times you may swap the numbers round. 3 × 8 = 8 × 3 and 7 + 5 = 5 + 7.
- Group: with plus and times you may choose which two you do first. Look for friends that make 10, 100 or a round number.
- With minus and divide it does not work: 9 − 4 is not 4 − 9.
Clever counting
Choose “Swap” or “Group” and try.
If you have 9 sweets and give 4 away, you have 5 left. But if you have 4 sweets, you cannot give 9 away. The order matters.
Break up, and the numbers 0 and 1
A big times sum is easy if you break up the big number: 6 × 14 = 6 × 10 + 6 × 4 = 60 + 24 = 84.
Break up
Change the numbers and watch the rectangle break into two parts.
Number + 0 = the same number · Number × 1 = the same number · Number × 0 = 0
Play: multiples, factors and tricks
Choose the answer
Think of the times tables and the three tricks.
Correct: 0Check yourself
- Multiples of 4: 4, 8, 12, 16 … (the 4 times table).
- Factors of 12: 1, 2, 3, 4, 6, 12. A prime number has only two factors: 1 and itself.
- Swap and group work with + and ×, not with − and ÷.
- Break up: 6 × 14 = 6 × 10 + 6 × 4. Number × 1 = the number; number × 0 = 0.
Write these points in your maths book. Read them again the night before the test.
Quick questions
Tap an answer. If you get one wrong, read why and go back to that step. You get new questions every time.
You ticked all 5 steps! Now you are ready for the quiz.- Practice sheet for this classQuestions + memo · 2 A4 pagesPractice sheet
- Numbers14 pages · PDFPaperMemo
Ready for more? The Grade 4 quiz on multiples, factors and properties gives you new questions every time.
- One step a day is enough. Ten calm minutes work better than an hour the night before the test.
- Play “Buzz”: count out loud together and say “buzz” for every multiple of 3 (or 4, or 7).
- Ask your child to tell you the rule in their own words. If they can explain it, they understand it.
- The ticks (“I understand this”) are saved on this device only. We never ask for names or emails.
Follows CAPS for Grade 4 Maths. Always check your teacher’s notes and textbook too.