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20 Jun 2018

BASIC MATHEMATICAL CONCEPT 1.3: FACTORS, MULTIPLES AND PRIMES

1.2  FACTORS, MULTIPLES AND PRIMES

The Factors of a number are the whole numbers that divide the number exactly without a remainder. For example, the factors of 12 are: 1, 2, 3, 4, 6 and 12 itself.

Note: 1 is a factor of any number and a number is a factor of itself.

Multiples:

A multiple of a whole number is obtained by multiplying it by any whole number. For example, 18 is a multiple of 3 and 6 because $18=3×6.$

Further Example:

The multiples of 4 are: 4, 8, 12, 16, 20, 24, 28, and so on. This is because

$4×1=4$,
$4×2=8$,
$4×3=12$,
$4×4=16$,
$4×5=20$ and so on.

Similarly, the multiples of 3 are: 3, 6, 9, 12, 15, 18, etc.

Prime Numbers:

A prime number is a number that has only two factors; 1 and the number itself. Meaning that only 1 and itself can divide it without a remainder. For example, 23 have only two factors, i.e. 1 and 23.

Examples of prime numbers are 2, 3, 5, 7, 11, 13, 17 etc.

Prime Factors:

A prime factor is a factor that is a prime number. For example, out of the factors of 12 which are: 1, 2, 3, 4, 6 and 12, only 2 and 3 are the prime factors of 12.

Product of prime factors

Every number can be written as a product of prime numbers.

Remember: ‘product’ means ‘times’ or ‘multiply’.

For example,

$40 = 2 × 2 ×2 × 5$,
$126 = 2 × 3 × 3 × 7$

How do we write a number as a product of its prime factors?

Example 1:

Write 24 as a product of its prime factors.

Solution

There are lots of ways to solve this. Here are three methods:

Method 1:

We start with the smallest prime number that divides 24, which is 2.

So we can write 24 as:

24 = 2 x 12

Now think of the smallest prime number that can divide 12. We can still use 2, and then write the 12 as:

12 = 2 x 6.

Hence our $24= 2×2×6$

Since the smallest prime number 2 can still divide 6 so we have:

$6 = 2×3$

Hence our   $24= 2×2×2×3$, which are all prime numbers.

In short, we would write the solution as:

$24=2×12$
$=2×2×6$
$=2×2×2×3$

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