Factors and Multiples
"Discover how numbers divide cleanly and build endless multiplication families."
A Today you'll learn
- Understand factors as numbers that divide evenly into another number with zero remainder
- Understand multiples as products found in multiplication tables
- Distinguish between prime numbers (exactly two factors) and composite numbers
B Let's understand
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
A factor of a number is an exact divisor that divides the number completely without leaving any remainder. For example, 1, 2, 3, 4, 6, and 12 are all factors of 12 because 12 can be divided by each of them with zero remainder. A multiple of a number is the product obtained when that number is multiplied by any whole counting number. For instance, the multiples of 4 are 4, 8, 12, 16, 20, 24, and so on. Numbers with exactly two distinct factors (1 and the number itself) are called prime numbers (e.g., 2, 3, 5, 7, 11). Numbers with more than two factors are called composite numbers (e.g., 4, 6, 8, 9, 10). The number 1 is unique: it is neither prime nor composite.
C See it step by step
- Find pairs of numbers that multiply to 18: 1 × 18 = 18; 2 × 9 = 18; 3 × 6 = 18.
- The factors of 18 are 1, 2, 3, 6, 9, and 18.
- Since 18 has 6 factors (more than two), 18 is a composite number.
- Multiply 7 by 1, 2, 3, 4, and 5.
- 7 × 1 = 7; 7 × 2 = 14; 7 × 3 = 21; 7 × 4 = 28; 7 × 5 = 35.
- The first five multiples of 7 are 7, 14, 21, 28, and 35.
D Your turn
E Ready to practise?
Key idea 1
1 is a factor of every number; every number is a factor of itself.
Key idea 2
A number has a finite (limited) count of factors, but infinitely many multiples.
2 is the smallest prime number
2 is the smallest prime number, and the only even prime number.
Key idea 4
Common factors are factors shared by two or more numbers.
Key idea 5
The number 1 is neither prime nor composite.