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    how do you do the unique factorisation theorem? I don't get it ?? please help me
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    (Original post by mayu123)
    how do you do the unique factorisation theorem? I don't get it ?? please help me
    so basically just divide the number using prime numbers then write it up.

    for example using the "Unique factorisation theorem" as you put it on the number 200

    5 is a prime number so i can use that

     200 \div 5 = 40

     40 \div 5 =8

    2 is a prime number too so i can use that

    8 \div 2=4

    4 \div 2=2

    so now we count up how many times we had to divide the number 200 by prime numbers, we also need to include the last number which is 2 aswell

    so we have 2 5s and 3 2s so we can write this in the form 2^3 \times 5^2 =200
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    (Original post by mayu123)
    how do you do the unique factorisation theorem? I don't get it ?? please help me
    It's more commonly called the "fundamental theorem of arithmetic" - to prove this theorem, you need to make use of Euclid's Lemma. That is, p | ab \Rightarrow p | a \vee p | b.

    Use strong induction to show that every integer greater than 1 is a product of primes. The proof is quite elementary.

    The uniqueness part is slightly harder, assume an integer is a product of primes in two different ways: a = p_1\cdots p_n = q_1 \cdots q_m then we need to show that this is the same thing and m=n.

    Now use Euclid's Lemma on each p_i and q_i to show that p_i = q_i (up to relabelling).
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    (Original post by thefatone)
    so basically just divide the number using prime numbers then write it up.

    for example using the "Unique factorisation theorem" as you put it on the number 200

    5 is a prime number so i can use that

     200 \div 5 = 40

     40 \div 5 =8

    2 is a prime number too so i can use that

    8 \div 2=4

    4 \div 2=2

    so now we count up how many times we had to divide the number 200 by prime numbers, we also need to include the last number which is 2 aswell

    so we have 2 5s and 3 2s so we can write this in the form 2^3 \times 5^2 =200
    thanks for the most detailed answer thanks but I still don't get the last part ow u got the answer.
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    (Original post by mayu123)
    thanks for the most detailed answer thanks but I still don't get the last part ow u got the answer.
    \displaystyle 200 = 2 \times 100 = 2\times 2 \times 50 = 2 \times 2 \times 2 \times 25 = 2 \times 2 \times 2 \times 5 \times 5 = 2^3 \times 5^2
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    (Original post by mayu123)
    thanks for the most detailed answer thanks but I still don't get the last part ow u got the answer.
    (Original post by Zacken)
    \displaystyle 200 = 2 \times 100 = 2\times 2 \times 50 = 2 \times 2 \times 2 \times 25 = 2 \times 2 \times 2 \times 5 \times 5 = 2^3 \times 5^2
    ^^ this is exactly correct
    200= 5x40
    200= 5x5x8
    200= 5x5x2x4
    200= 5x5x2x2x2
    200= 5²x2³
    ^^ write this one because it's in its simplest form
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    (Original post by thefatone)
    ^^ this is exactly correct
    200= 5x40
    200= 5x5x8
    200= 5x5x2x4
    200= 5x5x2x2x2
    200= 5²x2³
    ^^ write this one because it's in its simplest form
    okay ty fo rhelp
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    (Original post by Zacken)
    \displaystyle 200 = 2 \times 100 = 2\times 2 \times 50 = 2 \times 2 \times 2 \times 25 = 2 \times 2 \times 2 \times 5 \times 5 = 2^3 \times 5^2
    ty for lot of detail made sense now
 
 
 
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