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Prime Factorization

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    Write the prime factorization
    of 75.
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    Write your answer using
    exponential notation.
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    So we have a couple of
    interesting things here.
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    Prime factorization, and they
    say exponential notation.
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    We'll worry about the
    exponential notation later.
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    So the first thing we have to
    worry about is what is even a
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    prime number?
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    And just as a refresher, a
    prime number is a number
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    that's only divisible by itself
    and one, so examples of
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    prime numbers-- let me write
    some numbers down.
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    Prime, not prime. Not prime.
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    So 2 is a prime number.
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    It's only divisible
    by 1 and 2.
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    3 is another prime number.
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    Now, 4 is not prime,
    because this is
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    divisible by 1, 2 and 4.
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    We could keep going.
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    5, well, 5 is only divisible
    by 1 and 5, so 5 is prime.
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    6 is not prime, because it's
    divisible by 2 and 3.
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    I think you get the
    general idea.
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    You move to 7, 7 is prime.
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    It's only divisible
    by 1 and 7.
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    8 is not prime.
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    9 you might be tempted to say
    is prime, but remember, it's
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    also divisible by 3,
    so 9 is not prime.
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    Prime is not the same thing
    as odd numbers.
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    Then if you move to 10,
    10 is also not prime,
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    divisible by 2 and 5.
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    11, it's only divisible
    by 1 and 11, so 11 is
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    then a prime number.
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    And we could keep going
    on like this.
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    People have written computer
    programs looking for the
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    highest prime and all of that.
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    So now that we know what
    a prime is, a prime
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    factorization is breaking up
    a number, like 75, into a
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    product of prime numbers.
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    So let's try to do that.
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    So we're going to start with
    75, and I'm going to do it
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    using what we call a
    factorization tree.
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    So we first try to find just the
    smallest prime number that
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    will go into 75.
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    Now, the smallest prime
    number is 2.
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    Does 2 go into 75?
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    Well, 75 is an odd number, or
    the number in the ones place,
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    this 5, is an odd number.
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    5 is not divisible by 2, so
    2 will not go into 75.
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    So then we could try 3.
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    Does 3 go into 75?
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    Well, 7 plus 5 is 12.
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    12 is divisible by 3, so
    3 will go into it.
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    So 75 is 3 times
    something else.
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    And if you've ever dealt with
    change, you know that if you
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    have three quarters, you have
    75 cents, or if you have 3
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    times 25, you have 75.
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    So this is 3 times 25.
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    And you can multiply this out
    if you don't believe me.
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    Multiple out 3 times 25.
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    Now, is 25 divisible by--
    you can give up on 2.
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    If 75 wasn't divisible by 2,
    25's not going to be divisible
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    by 2 either.
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    But maybe 25 is divisible
    by 3 again.
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    So if you take the digits
    2 plus 5, you get 7.
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    7 is not divisible by 3, so 25
    will not be divisible by 3.
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    So we keep moving up: 5.
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    Is 25 divisible by 5?
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    Well, sure.
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    It's 5 times 5.
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    So 25 is 5 times 5.
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    And we're done with our prime
    factorization because now we
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    have all prime numbers here.
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    So we can write that 75
    is 3 times 5 times 5.
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    So 75 is equal to 3
    times 5 times 5.
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    We can say it's 3 times 25.
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    25 is 5 times 5.
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    3 times 25, 25 is 5 times 5.
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    So this is a prime
    factorization, but they want
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    us to write our answer using
    exponential notation.
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    So that just means, if we have
    repeated primes, we can write
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    those as an exponent.
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    So what is 5 times 5?
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    5 times 5 is 5 multiplied
    by itself two times.
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    This is the same thing as
    5 to the second power.
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    So if we want to write our
    answer using exponential
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    notation, we could say this is
    equal to 3 times 5 to the
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    second power, which is the
    same thing as 5 times 5.
Title:
Prime Factorization
Description:

U02_L1_T3_we3 Prime Factorization

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Video Language:
English
Duration:
04:09
Christi Rockwell edited English subtitles for Prime Factorization
Christi Rockwell edited English subtitles for Prime Factorization
Christi Rockwell edited English subtitles for Prime Factorization
Christi Rockwell edited English subtitles for Prime Factorization
vaan.auger edited English subtitles for Prime Factorization
vaan.auger edited English subtitles for Prime Factorization
vaan.auger edited English subtitles for Prime Factorization
vaan.auger edited English subtitles for Prime Factorization
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