Counting in sixes gives 6, 12, 18, 24 and onward.
Multiple is what you get when you multiply a number by a whole number.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Factors and multiples get mixed up
A factor of 12 is never bigger than 12. A multiple of 12 is never smaller.
They point at each other
3 is a factor of 12, and 12 is a multiple of 3. One statement, read from either end.
Common multiples
12 appears in both the threes and the fours, so it is a multiple of both.
Multiples are what you get by counting on
The multiples of 6 are 6, 12, 18, 24, 30 and so on — the answers in the 6 times table. There is no largest multiple; the list goes on forever. This is the opposite of factors, which are a short finite list.
Factors and multiples are opposite directions
3 is a factor of 12; 12 is a multiple of 3. The same relationship, described from either end. Confusing the two words is common, and the fix is to remember that factors are smaller and multiples are bigger.
Common multiples
Numbers that appear in two lists are common multiples: 12, 24 and 36 are all multiples of both 4 and 6. The smallest of these, 12, is the least common multiple. This is the number you will need when adding fractions with unlike denominators.
Quick tests for multiples
A number is a multiple of 2 if it ends in an even digit; of 5 if it ends in 0 or 5; of 10 if it ends in 0; of 3 if its digits add to a multiple of 3. That last one is genuinely surprising — 471 has digits summing to 12, so it is a multiple of 3.
Step 2: Try It Yourself
Tap and try it out.
The ringed squares are the multiples of 6. They land in a pattern.
Step 3: Watch an Example
One step at a time.
Watch Ana Find a Common Multiple
Ana looks for a number in both the fours and the sixes.
- Step 1
She lists the fours: 4, 8, 12, 16, 20, 24.
Step 4: Your Turn
Practice makes it stick.
The Buses
Problem 1 of 2
One bus comes every 4 minutes, another every 6. After how many minutes do both come together?
minutes
The Packs
Problem 2 of 2
Buns come in 8s and sausages in 6s. What is the smallest number that matches?
each
Factor or Multiple?
1 of 4
What is the 5th multiple of 7?
2 of 4
Is 45 a multiple of 9?
3 of 4
Smallest common multiple of 3 and 5?
4 of 4
Can a multiple of 8 be smaller than 8?
Step 5: Quick Check
Show what you know.
Question 1 of 2
Smallest common multiple of 4 and 10?
Question 2 of 2
Which is never bigger than the number itself?
What You Learned
- A multiple is what you get by multiplying.
- Factors are never bigger; multiples are never smaller.
- A common multiple appears in both lists.