Skip-counting gives you multiples. Counting by 6 gives 6, 12, 18, 24, … Each of these is 6 times a whole number. It is the other side of factor pairs.
Key idea
A multiple of 6 is $6 \times$ a whole number: 6, 12, 18, 24, 30, … A factor of 12 divides 12 evenly: 1, 2, 3, 4, 6, 12. Since $3 \times 4 = 12$, 12 is a multiple of 3 and of 4, and 3 and 4 are factors of 12.
Why it works
"Factor" and "multiple" describe the same multiplication from two sides. In $3 \times 4 = 12$, the small numbers (3 and 4) are factors, and the product (12) is the multiple. Multiples of a number are never smaller than it; factors are never bigger.
Worked example: Is it a multiple?
Is 56 a multiple of 8?
- Skip-count by 8: 8, 16, 24, 32, 40, 48, 56.
- Or use a fact: $8 \times 7 = 56$.
Answer: Yes, 56 is a multiple of 8.
Worked example: Factor or multiple?
Which of 2, 3, 24 and 36 are multiples of 12?
- $12 \times 2 = 24$ and $12 \times 3 = 36$, so 24 and 36 are multiples.
- 2 and 3 are smaller than 12; they are factors of 12, not multiples.
Answer: 24 and 36
Common mistake
Mixing the two words, like calling 2 and 3 "multiples of 12." Ask: is it bigger, made by multiplying 12 (a multiple)? Or smaller, dividing into 12 (a factor)?