How to Use Prime Factor Trees to find Prime Factors #5

00:06:01
https://www.youtube.com/watch?v=FL4MPqfbFbw

الملخص

TLDRThe video provides a detailed explanation of what prime factors are and how to find them using a process known as a factor tree. A prime factor is defined as a factor of a number that is a prime number itself. To express a number as a product of its prime factors, you can use factor trees, which involve breaking the number down into smaller factors until all factors are prime. For instance, the video discusses finding prime factors of the number 12, which are 2 and 3, via multiplication that results in 12 as 2*2*3. For more complex numbers like 220, a factor tree can help decompose it into 2, 2, 5, and 11. The order of factorization doesn’t matter, as any correct method will lead to the same set of prime factors. The video also covers the concept of prime factorization in which every number is expressed as a product of its prime factors, such as 112, which is 2^4 * 7.

الوجبات الجاهزة

  • 🔢 Prime factors are factors that are also prime numbers.
  • 🧮 Factor trees help break down numbers into prime factors.
  • 📚 Use prime factorization to express numbers as a product of prime factors.
  • 🔄 The order in which you factorize doesn’t change the prime factors obtained.
  • 🔍 Factor trees involve splitting numbers into factors and circling the primes.
  • ✏️ Example: 220 breaks down into 2, 2, 5, and 11 - that's 2² * 5 * 11.
  • ✏️ Example: 112 breaks down into 2⁴ * 7 using a factor tree.
  • 💡 Each step in factorization should result in prime factors for simplicity.
  • 📐 Understanding factorization is key for solving prime factor-related math problems.
  • 📘 The process demonstrated is useful for exam questions about prime factors.

الجدول الزمني

  • 00:00:00 - 00:06:01

    The video introduces the concept of prime factors and explains how to find them using factor trees. A prime factor is a factor of a number that is also a prime number. For example, the number 12 has factors 1, 2, 3, 4, 6, and 12, but only 2 and 3 are prime factors. The video explains that in exams, you'll often need to express a number as a product of its prime factors, which involves finding a set of prime factors that multiply to give the original number. To express 12 as a product of its prime factors, it needs to be written as 2 times 2 times 3, which equals 12."

الخريطة الذهنية

Mind Map

الأسئلة الشائعة

  • What is a prime factor?

    A prime factor is a factor of a number that is also a prime number.

  • How do you find prime factors using a factor tree?

    To use a factor tree, write the number at the top, then break it down into factors, circling the prime numbers and reducing non-prime numbers further until all factors are prime.

  • Can you give an example of prime factorization using a factor tree?

    For example, to prime factorize 220, you can split it into 2 and 110, then 110 into 10 and 11, and finally 10 into 2 and 5, giving 2, 2, 5, and 11 as prime factors.

  • Does the order of factorization affect the final prime factors?

    No, the order of factorization does not affect the final set of prime factors; different paths will lead to the same primes.

  • What is the final prime factorization of the number 220?

    The prime factorization of 220 is 2^2 * 5 * 11.

  • What is the purpose of circling numbers in the factor tree?

    Circling numbers in the factor tree indicates that they are prime factors and need no further division.

  • What does expressing a number as a product of its prime factors mean?

    It means finding prime numbers that multiply together to give the original number.

  • What is the prime factorization of 112 using a factor tree?

    The prime factorization of 112 is 2^4 * 7.

  • What does the term 'prime factorization' refer to?

    Prime factorization refers to the process of breaking down a number into a product of its prime factors.

  • Is the method applicable to any number?

    Yes, the factor tree method can be applied to any number to determine its prime factors.

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التمرير التلقائي:
  • 00:00:00
    [Music]
  • 00:00:04
    in today's video we're looking at what
  • 00:00:07
    prime factors are
  • 00:00:09
    and also how we can find them using
  • 00:00:11
    factor trees
  • 00:00:14
    all we mean by a prime factor
  • 00:00:16
    is a factor that's also a prime number
  • 00:00:23
    so if we took the number 12
  • 00:00:25
    which has the factors 1 2 3
  • 00:00:29
    4 6 and 12
  • 00:00:32
    2 and 3 would be considered prime
  • 00:00:35
    factors
  • 00:00:36
    because they're both prime numbers
  • 00:00:38
    and factors of 12.
  • 00:00:44
    when you get questions about this sort
  • 00:00:45
    of topic in the exam
  • 00:00:47
    they'll normally ask you to write a
  • 00:00:49
    number as a product of its prime factors
  • 00:00:54
    and what they mean by this is that they
  • 00:00:56
    want you to find a set of prime factors
  • 00:01:00
    that multiply together to give that
  • 00:01:02
    number
  • 00:01:04
    so if we were asked to write 12 as a
  • 00:01:07
    product of its prime factors
  • 00:01:10
    we'd need to come up with a set of
  • 00:01:12
    numbers that multiply together to make
  • 00:01:14
    twelve
  • 00:01:16
    we already know that two and three are
  • 00:01:19
    prime factors of twelve
  • 00:01:21
    but we can't just write two times three
  • 00:01:24
    because two times three is six not
  • 00:01:27
    twelve
  • 00:01:29
    instead we'd have to do two times two
  • 00:01:32
    times three
  • 00:01:33
    which are still all prime numbers
  • 00:01:36
    but now do multiply to give us twelve
  • 00:01:42
    if you want to find the prime factors of
  • 00:01:44
    more complicated numbers though
  • 00:01:47
    like you might need to in the exam
  • 00:01:49
    you'll need to use a method called a
  • 00:01:50
    factor tree
  • 00:01:52
    to understand how these things work
  • 00:01:55
    let's imagine we were asked to write 220
  • 00:01:58
    as a product of its prime factors
  • 00:02:01
    the first step is to write the number
  • 00:02:04
    whose prime factors you're trying to
  • 00:02:06
    find
  • 00:02:07
    so 220 at the very top of the page
  • 00:02:10
    then we can start to factorize it by
  • 00:02:13
    splitting it up into a factor
  • 00:02:15
    for example here we might do 110 and 2.
  • 00:02:20
    if one of these is a prime number and
  • 00:02:23
    hence a prime factor like two is
  • 00:02:26
    then we can circle it
  • 00:02:28
    and leave it alone for now
  • 00:02:30
    but if it's not a prime number like 110
  • 00:02:34
    then we have to factorize it again
  • 00:02:37
    into say 11 and 10.
  • 00:02:40
    11 is a prime number
  • 00:02:42
    so we circle that
  • 00:02:44
    and then split the 10 into 5 and 2
  • 00:02:48
    which also both prime numbers
  • 00:02:50
    so we can circle them both
  • 00:02:53
    now that we've finished factorizing it
  • 00:02:56
    we can write out all our prime factors
  • 00:02:59
    so 2
  • 00:03:00
    2
  • 00:03:01
    5 and 11.
  • 00:03:04
    and it's normally best to put them in
  • 00:03:05
    ascending order like this
  • 00:03:07
    which just means from smallest to
  • 00:03:09
    biggest
  • 00:03:11
    so basically we found that 220
  • 00:03:15
    equals 2 times two times five times
  • 00:03:18
    eleven
  • 00:03:20
    and as two occurs twice we should
  • 00:03:23
    rewrite it as two squared times five
  • 00:03:26
    times eleven
  • 00:03:31
    now one thing to clarify here is that it
  • 00:03:33
    doesn't actually matter which way you
  • 00:03:35
    factorize it
  • 00:03:37
    you will always end up with the same
  • 00:03:39
    prime factors
  • 00:03:41
    for example we could have split the 220
  • 00:03:44
    into 10 and 22
  • 00:03:47
    then split the 10 into 5 and 2
  • 00:03:51
    and split the 22
  • 00:03:53
    into 2 and 11.
  • 00:03:56
    we'd still have ended up with 2 2 5 and
  • 00:04:00
    11 as our prime factors
  • 00:04:04
    so don't worry about which way you
  • 00:04:06
    factorize it
  • 00:04:07
    as long as each time you're making a
  • 00:04:09
    correct factor
  • 00:04:11
    then you'll end up with the same answer
  • 00:04:13
    at the end
  • 00:04:17
    let's try one more where we're asked to
  • 00:04:19
    express 112 as a product of its prime
  • 00:04:22
    factors
  • 00:04:24
    the word express basically just means
  • 00:04:27
    write or show
  • 00:04:28
    so we're doing exactly the same thing as
  • 00:04:31
    we were in the previous questions
  • 00:04:34
    to start we put 112 at the top
  • 00:04:37
    and then we just split it into a factor
  • 00:04:40
    and the easiest pair if it's an even
  • 00:04:42
    number will generally be two
  • 00:04:45
    and whatever else you need
  • 00:04:48
    in this case 56
  • 00:04:50
    so we can circle the two
  • 00:04:52
    and then split the 56 into two and 28
  • 00:04:57
    then the 28 can go into 2 and 14
  • 00:05:01
    and finally the 14 can go into 2 and 7.
  • 00:05:06
    so we can express 112
  • 00:05:08
    as two times two times two times two
  • 00:05:12
    times seven
  • 00:05:14
    and then we can rewrite it as two to the
  • 00:05:16
    power of four times seven
  • 00:05:20
    one last thing to mention is that this
  • 00:05:22
    whole process we've been covering in
  • 00:05:24
    this video is sometimes called prime
  • 00:05:27
    factorization
  • 00:05:28
    which just means to rewrite a number as
  • 00:05:31
    a product of its prime factors
  • 00:05:35
    so in this last question we basically
  • 00:05:38
    did the prime factorization of 112.
  • 00:05:46
    anyway that's everything for this video
  • 00:05:48
    so hope you enjoyed it and found it
  • 00:05:50
    useful in some way and cheers for
  • 00:05:52
    watching
الوسوم
  • prime factors
  • factor trees
  • prime numbers
  • product of prime factors
  • factorization
  • exam preparation
  • math concepts
  • prime factorization
  • examples
  • factor tree method