A student asked to list the multiples of 6 writes: 1, 2, 3, 6. What mistake did they make?
AThey forgot to include 0 and 12
BThey listed the factors of 6, not the multiples
CThey confused 6 with an even number
DThey counted backward instead of forward
The student listed the factors of 6 (the numbers that divide evenly into 6) rather than the multiples (the numbers you get by multiplying 6 by whole numbers). The multiples of 6 are 6, 12, 18, 24, 30... — found by skip-counting by 6 or computing 6×1, 6×2, 6×3, and so on. Factors and multiples are related but opposite: factors of a number are smaller or equal to it, while multiples are greater than or equal to it.
Question 2 Multiple Choice
Which statement correctly describes the multiples of 7?
AThe list of multiples of 7 eventually ends when you run out of multiplication facts
BAll multiples of 7 are odd numbers
CThe multiples of 7 are 7, 14, 21, 28, 35... continuing without end
DThe multiples and factors of 7 are the same numbers
Multiples go on forever because you can always multiply 7 by a larger whole number to get another multiple — there is no largest one. Option A is wrong because multiplication facts are just a starting list; the concept extends infinitely. Option B is wrong because multiples of 7 include even numbers (14, 28, 42...). Option D confuses multiples with factors: the factors of 7 are only 1 and 7 (since 7 is prime), while its multiples are the infinite list 7, 14, 21...
Question 3 True / False
Every multiple of 6 is also a multiple of 3.
TTrue
FFalse
Answer: True
True. Because 6 = 2 × 3, any number produced by multiplying 6 by a whole number automatically contains 3 as a factor. For example: 6×4 = 24, and 24 = 3×8. This is a general pattern: if one number is a multiple of another (6 is a multiple of 3), then all multiples of the larger number are also multiples of the smaller one. Exploring these patterns on a hundreds chart makes them visually obvious.
Question 4 True / False
A multiple of a number is typically smaller than the number itself.
TTrue
FFalse
Answer: False
False — it's the opposite. Multiples of a number are always greater than or equal to the number (the first multiple is n×1 = n itself, and all others are larger). It is *factors* that are smaller than or equal to the number. This is the most persistent confusion between factors and multiples: factors divide in, multiples build out.
Question 5 Short Answer
12 is both a multiple of 4 and a multiple of 3. A student asks: 'Does that make 12 special?' How would you explain what this means mathematically?
Think about your answer, then reveal below.
Model answer: 12 is a common multiple of 4 and 3 — a number that appears in both their multiple lists. This is significant because it means 12 can be divided evenly by both 3 and 4. The smallest number that two numbers share as a multiple is called the least common multiple (LCM), which becomes important when adding fractions with different denominators.
When two numbers share a multiple, that shared value lies at an intersection of their multiplication patterns. For 3 and 4, the common multiples are 12, 24, 36... (every multiple of 12). Understanding common multiples is the foundation for finding least common denominators — so recognizing that 12 appears in both the 3-list and the 4-list is not trivial, but a preview of a core fractions skill.