Imagine you have 12 laddoos and you want to arrange them in equal rows. You can make 1 row of 12, 2 rows of 6, 3 rows of 4, 4 rows of 3, 6 rows of 2, or 12 rows of 1. The numbers 1, 2, 3, 4, 6, and 12 are all factors of 12 because they divide 12 exactly without any remainder.
Now let us learn about factors, multiples, and some special types of numbers!
A factor is a number that divides another number exactly (with no remainder).
To find the factors of a number, think of all the pairs of numbers that multiply to give that number.
Find all factors of 18:
18 = 1 × 18 → so 1 and 18 are factors
18 = 2 × 9 → so 2 and 9 are factors
18 = 3 × 6 → so 3 and 6 are factors
4 does not divide 18 exactly. 5 does not divide 18 exactly.
Factors of 18 = 1, 2, 3, 6, 9, 18
A multiple is the result you get when you multiply a number by 1, 2, 3, 4, 5, and so on.
Multiples are like the numbers in a multiplication table.
Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40
(4×1=4, 4×2=8, 4×3=12, 4×4=16, 4×5=20, 4×6=24, 4×7=28, 4×8=32, 4×9=36, 4×10=40)
Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70
Common factors are factors that two or more numbers share.
Factors of 12: 1, 2, 3, 4, 6, 12. Factors of 18: 1, 2, 3, 6, 9, 18.
Common factors of 12 and 18: 1, 2, 3, 6 (these appear in both lists).
Common multiples are multiples that two or more numbers share.
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30...
Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36...
Common multiples of 3 and 4: 12, 24, 36...
A prime number has exactly 2 factors: 1 and itself. It cannot be divided evenly by any other number.
Examples: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29
A composite number has more than 2 factors. It can be divided by numbers other than 1 and itself.
Examples: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18
There are 15 players in a cricket squad. Can they be divided into equal groups? Factors of 15 = 1, 3, 5, 15. So they can form 3 groups of 5 or 5 groups of 3.
Rani has 24 barfis. She wants to share them equally among her friends. She can share among 2 friends (12 each), 3 friends (8 each), 4 friends (6 each), 6 friends (4 each), 8 friends (3 each), or 12 friends (2 each). All these are factors of 24.
| Word | Meaning |
|---|---|
| Factor | A number that divides another number exactly with no remainder |
| Multiple | The result of multiplying a number by 1, 2, 3, 4... |
| Common factor | A factor shared by two or more numbers |
| Common multiple | A multiple shared by two or more numbers |
| Prime number | A number with exactly 2 factors: 1 and itself |
| Composite number | A number with more than 2 factors |
Finished learning? Now test what you know!