Page 98 - Start Up Mathematics_4

Try 3 → 3 × 8 = 24, so 3 and 8 are factors

Try 4 → 4 × 6 = 24, so 4 and 6 are factors
Try 5 → 5 × ? = 24, not possible

Try 6 → 6 × 4 = 24 → We will stop here since the factors are repeating.
So, the factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24.

Properties of factors

1. The smallest factor of every number is 1. For example, 2 = 1 × 2, 3 = 1 × 3, 7 = 1 × 7.

2. Every number is a factor of itself. For example, factors of 27 are 1, 3, 9 and 27.

3. Factors of a number are always smaller than or equal to the number. For example, the
factors of 12 cannot be greater than 12.
4. A number can have only a limited number of factors. For example, 1, 2, 3 and 6 are
the only factors of 6.

5. 1 is the only number with one factor.
Before we study more about factors, let’s define two types of numbers.

Number

Prime Number Composite Number

1. It has only two factors, 1 and itself. 1. It has more than two factors.
2. It cannot be divided exactly 2. It can be divided exactly
by any other number other than 1 by its factors.
and itself.
For example, 2, 3, 5, 7, 11 are For example, 4, 6, 8, 9, 10 are
prime numbers. composite numbers.

Remember

• The smallest prime number is 2. A Challenge!
• The only even prime number is 2. All other even
numbers are composite numbers. How many prime numbers are
• 0 and 1 are neither prime nor composite numbers. there between 1 and 100?

Prime Factorization

Factorization means writing a number as a product of its factors.
We can write every composite number as a product of factors that are prime numbers. This
is called prime factorization.

Prime factors can be obtained by two methods: (1) Factor Tree Method, (2) Division Method.

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