wot's prime factorisation?

Question

as far as i know prime number is a number that does not have any factors...other than 1 and itself , then what the hell is this prime factorisation? can u kindly give me couple of examples such that the concept becomes clear....thanx

Answer 1

Prime Factorization There are different methods which can be utilized to find the prime factorization of a number. One way is to repeatedly divide by prime numbers: EXAMPLE 1. Prime factorization of 96 (by division): 96 ÷ 2 = 48 48 ÷ 2 = 24 24 ÷ 2 = 12 12 ÷ 2 = 6 6 ÷ 2 = 3 3 ÷ 3 = 1 96 = 2 * 2 * 2 * 2 * 2 * 3 -------------------------------------------------------------------------------- EXAMPLE 2. Prime factorization of 120 (by division): 120 ÷ 2 = 60 60 ÷ 2 = 30 30 ÷ 2 = 15 15 ÷ 3 = 5 5 ÷ 5 = 1 120 = 2 * 2 * 2 * 3 * 5

Prime Factorization The recognition of the fact that whole numbers bigger than 1 can be represented just one way as the product of primes is attributed to Euclid, who lived from 325 BC until he died in Alexandria, Egypt in 265 BC. By expressing numbers as products of prime factors, it is easy to find their Greatest Common Divisor, or their Least Common Multiple. First, you should know what a prime number is. It's a number that can't be expressed as the product (that means by multiplying together) smaller numbers. An example is 5. 5 can't be expressed as the product of any smaller numbers. Its only factors are 1 and 5. The Sieve of Eratosthanes can be used to find prime numbers. Using this method, we see that the first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29,

That looks like this: Find the prime factorization of 24: 24 ÷ 2 12 ÷ 2 6 ÷ 2 3 Now the last number written on each line is a prime number, so the method is not only easier to write, but it is clearer to see, as well. Again, the prime factorization of 24 is 2 × 2 × 2 × 3. This can be written as 23 × 3. The little "3" is called an exponent, and means that the 2 appears three times as a factor of 24. You say this "two to the power three times three". Now let's use the method with a different number. Find the prime factorization of 180: 180 ÷ 2 90 ÷ 2 45 ÷ 3 15 ÷ 3 5 So 180 = 22 × 32 × 5. One more example -- Find the prime factorization of 77: 77 ÷ 7 11 So 77 is 7 × 11

Answer 2

Example 1
28 = 4 x 7 = 2 x 2 x 7
The prime factors of 28 are 2 and 7.

Example 2
60 = 30 x 2 = 15 x 2 x 2 = 3 x 5 x 2 x 2
The prime factors of 60 are 2,3 and 5

Answer 3

To prime factor a number, begin dividing by the smallest possible prime and continue until the quotient is a prime number.

ex. 192 Prime Factorization

192 = 96 x 2

Now divide 96 by 2 = 48

192 = 48 x 2 x 2

Now divide 48 by 2 = 24

192 = 24 x 2 x 2 x 2

Now divide 24 by 2 = 12

192 = 12 x 2 x 2 x 2 x 2

Now divide 12 by 2 = 6

192 = 6 x 2 x 2 x 2 x 2 x 2

Now divide 6 by 2 = 3

192 = 3 x 2 x 2 x 2 x 2 x 2 x 2

And there's your answer.

Answer 4

Hi jayati,
It's not as difficult as you think.

As you know there are prime numbers and composite numbers. A prime has no factors but 1 and itself. But composite has other factors.

Lets take a composite number say 24.
Since it is composite numbers it has factors other than 1 and itslef.

Now lets express 24 as the product of its factors.

24 = 2*12 (you can write as 3*8 or 4*6 also)

Now look at 2*12. here 2 is prime and 12 is composite.

So 12 has factors.

So, 24= 2*2*6 (because 12=2*6)

Again 6 has factors 2 and 3

so 24 = 2*2*2*3

Now 24 is written as product of 4 factors and all the four are primes.

Any composite number (one which has factors other than 1 and itself) can be written as product of prime factors.

This process of expressing any composite number as product of primes is called prime factorisation.

Some examples:

Prime factorisation of 100 is 2*2*5*5

Prime factorisation of 125 is 5*5*5

that of 56 is 2*2*2*7.

Hope this is useful.

Answer 5

To prime factor a number, begin dividing by the smallest possible prime and continue until the quotient is a prime number.

ex. 192 Prime Factorization

192 = 96 x 2

Now divide 96 by 2 = 48

192 = 48 x 2 x 2

Now divide 48 by 2 = 24

192 = 24 x 2 x 2 x 2

Now divide 24 by 2 = 12

192 = 12 x 2 x 2 x 2 x 2

Now divide 12 by 2 = 6

192 = 6 x 2 x 2 x 2 x 2 x 2

Now divide 6 by 2 = 3

192 = 3 x 2 x 2 x 2 x 2 x 2 x 2

And there's your answer.

Answer 6

Dividing a number with prima factors till we get a prime number is calles prime factorisation


99 DIVIDED BY 3 = 33
33 DIVIDED BY 3 = 11
11 is a prime number

A number which have no other factors exept 1 and itself is a prime number .
Numbers which have more than these factors are called composite numbers .

Now see 3 X 3 X 11 = 99

99 Can be prime factorised by by this way .

Answer 7

By Fundamental theorem of arithmatic : every positive integer greater than 1 can be written uniquely as a prime or as the product of two or more primes where the prime factors are witten in order of nondecreasing size.

examples: the prime factorization of 100,999 are as follows
100=2^2X5^2
999=3^3X37

Answer 8

Prime factorization is a technique to represent any number by only using prime numbers. One technique is to start by dividing by the lowest prime factor and working until all factors are prime numbers

example

96/[2] =48
48/[2]=24
24/[2]=12
12/[2]=6
6/[2]=[3] three is prime so this is the last factor

which shows 96 can be represented by 2*2*2*2*2*3

260/[2]=130
130/[2]=65
65/[5]=[13]

which shows 260 can be represented by 2*2*5*13

Answer 9

Prime Factorization Defined

www.purplemath.com/modules/factnumb.htm

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Answer 10

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