Skills / Ages 11 to 14 / Math
Factors and multiples
Listing every number that divides a given number with nothing left over, which are its factors, and listing the numbers you land on when you skip count by it, which are its multiples.
Why it matters
The book finds the greatest common factor and the least common multiple by writing out two lists and looking for a match. There is no shortcut in that lesson. The lists are the method. A child who can build a complete factor list and a clean list of multiples has done most of the work before the lesson starts.
What it looks like when your child can do it
- Asked for the factors of 36, your child works in pairs, 1 and 36, 2 and 18, 3 and 12, 4 and 9, 6 and 6, and stops there.
- Your child lists the multiples of 8 by skip counting: 8, 16, 24, 32, 40, 48.
- Your child knows that 7 x 12 = 84 means 7 is a factor of 84 and 84 is a multiple of 7.
How to teach it at the kitchen table
- 01
Factors divide in, multiples grow out
A factor of 20 divides 20 with nothing left over, so every factor is 20 or smaller. A multiple of 20 is 20 times a whole number: 20, 40, 60 and on. The factor list ends, and the multiples go on forever.
- 02
Build rectangles with pennies
Take 12 pennies and lay them in equal rows. 1 row of 12, 2 rows of 6 and 3 rows of 4 all work, and 5 rows do not. Every rectangle your child makes is a factor pair.
- 03
List factors in pairs from 1 upward
For 24, write 1 and 24, then 2 and 12, then 3 and 8, then 4 and 6. Try 5: it does not fit. The next pair would be 6 and 4, already written, so the pairs have met and the list is done.
- 04
List multiples by skip counting
The multiples of 6 are 6, 12, 18, 24, 30 and on. Say them out loud. Skip counting is the times table in order, so strong facts make this quick.
You will need: A pile of 12 to 36 pennies or dried beans · Paper and a pencil
Try it together
Try 1
Ask for every factor of 36.
Listen for 1, 2, 3, 4, 6, 9, 12, 18, 36. Watch that your child works in pairs and stops at 6 and 6. A missing 9 or 18 usually means the pairs were not written together.
Try 2
Ask for every factor of 20.
Listen for 1, 2, 4, 5, 10, 20. Your child should try 3 along the way and find that it leaves a remainder of 2.
Try 3
Ask for the first six multiples of 8.
Listen for 8, 16, 24, 32, 40, 48. If your child writes 1, 2, 4, 8, those are the factors of 8, and the two words need sorting out.
Try 4
Ask whether 6 is a factor of 44.
Listen for No. 44 ÷ 6 is 7 with 2 left over, and a factor leaves nothing over. The factors of 44 are 1, 2, 4, 11, 22 and 44.
Try 5
Ask which numbers are factors of both 12 and 18.
Listen for 1, 2, 3 and 6. This is the stretch question and a preview of the book's lesson, where the greatest of these, 6, gets its own name.
Watch for
- Mixing up the two words. A quick check: factors are never bigger than the number, and multiples are never smaller.
- Stopping a factor list before the pairs meet, and losing the bigger factors, like 18 in the list for 36.
If it is not there yet
- Back up to rows of pennies or beans. Building every rectangle for 12, 16 and 18 shows what a factor pair is before the lists go on paper.
- If the lists come slowly, the multiplication facts need work first. Skip counting by 6, 7 and 8 out loud for a few days helps.
A few days of this is normal, and it is time well spent. The lesson will still be there, and it will go faster.
Where this skill comes up
Grade 6 Math Practice Workbook · Lesson 3
Greatest Common Factor, Least Common Multiple
Needs it because GCF and LCM are found by listing them.