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Chapter3 6 ½ –

Factor and Multiples

Factors
When a number is broken in two or more numbers which can divide this number
completely are called its factors.

As 7 × 3 = 21 Remember
So 7 and 3 are factors of 21. We should remember that 1 and the number
itself are the factor of all the numbers.
Similarly,
12 is divisible by 1,2,3,4,6 and 12 so all these numbers are the factors of 12.

Multiples

As per above example

7 × 3 = 21
Here 21 is the multiple of 7 and 3 inspite of this :
7, 14, 21, 28 .............. all are multiples of 7.

Similarly,
3, 6, 9, 12, 15, 18, 21 .............. all are multiples of 3.

Prime Numbers and Composite Numbers
A prime number is a whole number that has exactly two factors, 1 and number
itself.

The Sieve of Eratosthenes is an ancient algorithm that can help us find all
prime numbers up to any given limit.

The following example illustrates how the Sieve of Eratosthenes, can be used to

find all the prime numbers that are less than 100.
Step 1 : Write the numbers 1 to 100 in ten rows.

Step 2 : Cross out 1 because 1 is not a prime.
Step 3 : Circle 2 and cross out all multiples of 2. (2, 4, 6, 8, 10, ........)

Step 4 : Circle 3 and cross out all multiples of 3. (3, 6, 9, 12, 15, ......)
Step 5 : Circle 5 and cross out all multiples of 5. (5, 10, 15, 20, .........)

Step 6 : Circle 7 and cross out all multiples of 7. (7, 14, 21, 28, .........)

Circle all the numbers that are not crossed out and they are the prime numbers
less than 100.

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Mathematics In Focus - 5