How to find Multiples and Factors #3

00:06:24
https://www.youtube.com/watch?v=PrSf78pnTyE

概要

TLDRIn this video, the concepts of multiples and factors are explained in a concise manner. Multiples of a number are the results of multiplying that number by integers, similar to values captured in its multiplication table, such as multiples of six being 6, 12, 18, etc. All multiples of a number are divisible by that number without any remainder. Factors of a number, on the other hand, are the integers that can be multiplied together to result in that original number, such as factor pairs for 28 being (2,14), (4,7), and (1,28). To find factors, identify all integers that divide the number without a remainder, which include the number itself. One can determine multiples by either multiplying the number by integers or repeatedly adding it to itself, while factors involve finding numbers that divide into it without leaving a remainder. The video provides methods to find both multiples and factors effectively and highlights key points to remember, such as avoiding confusion between the two and acknowledging that the number itself is both a multiple and a factor.

収穫

  • 🔢 Multiples are products of a number through multiplication - like times tables.
  • ➗ Factors are numbers that divide another number completely, leaving no remainder.
  • ✅ A number is both a multiple and a factor of itself.
  • 🔍 To check if a number is a multiple, divide it by the smaller number; no remainder means yes.
  • ✨ Factor pairs multiply to the original number, like (2, 14) for 28.
  • 📝 Keep repeating addition to find multiples or divide to uncover factors.
  • 🧠 Remember: multiples are bigger, factors are divisors.
  • 📉 List factors by finding pairs and ensuring full division.
  • ⚠️ Avoid mixing up multiples and factors in exams.
  • 📊 Factors list includes divisors like 1, 2, 4, etc., for 28.

タイムライン

  • 00:00:00 - 00:06:24

    The video introduces the concepts of multiples and factors, explaining that multiples are essentially the times tables of a number. For example, the first five multiples of six are 6, 12, 18, 24, and 30. All multiples of a number are divisible by that number without a remainder, which helps in identifying if a large number is a multiple of another by simply dividing. Similarly, factors are introduced through factor pairs, which multiply to give the original number. Factors of a number can also be identified by checking divisibility without a remainder. Steps to find all factors include checking starting from 1 to the number itself. The video concludes by comparing multiples and factors of a number, reminding viewers to distinguish between the two, also noting that the number itself is both a multiple and a factor.

マインドマップ

Mind Map

よくある質問

  • What are multiples?

    Multiples are the products of a number in its multiplication table.

  • How can you find if a large number is a multiple of another number?

    Divide the large number by the smaller number. If the result is a whole number, then it is a multiple.

  • What are factors?

    Factors of a number are whole numbers that can be multiplied together to produce that number.

  • How do you find the factors of a number?

    List all pairs of numbers that multiply to the given number and ensure they divide the number without leaving a remainder.

  • What's the relation between a number and its multiples?

    Multiples are larger numbers that result from multiplying the original number by whole numbers.

  • What's the relation between a number and its factors?

    Factors are numbers that when multiplied in pairs result in the original number.

  • Is 12 a multiple or factor of itself?

    Yes, 12 is considered both a multiple and a factor of itself.

  • How can you remember the difference between multiples and factors?

    Multiply to find multiples and divide to determine factors.

  • What are factor pairs?

    Factor pairs are sets of two numbers that, when multiplied together, result in the original number.

  • How can multiples and factors be confused?

    It's easy to confuse them since multiples involve multiplication, producing larger numbers, and factors involve division, dealing with divisors leading to the original number.

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  • 00:00:04
    in today's video we're going to look at
  • 00:00:06
    what multiples and factors are
  • 00:00:10
    if we start with multiples
  • 00:00:12
    these are basically the times tables of
  • 00:00:14
    a number
  • 00:00:16
    so the first five multiples of six
  • 00:00:19
    are six
  • 00:00:20
    because that's one times six
  • 00:00:23
    twelve
  • 00:00:24
    because that's two times six
  • 00:00:26
    eighteen
  • 00:00:27
    because that's three times 6 and so on
  • 00:00:31
    so the next ones would be 24 and 30.
  • 00:00:36
    because of this all the multiples of a
  • 00:00:38
    number will be divisible by that number
  • 00:00:42
    without any remainder
  • 00:00:44
    for example 18 divided by 6 is 3
  • 00:00:49
    with no remainder
  • 00:00:51
    so 18 must be a multiple of 6.
  • 00:00:56
    whereas if we looked at 19
  • 00:00:58
    19 over 6
  • 00:01:00
    is 3 with a remainder of 1
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    so it's not a multiple of 6
  • 00:01:06
    because it gave a remainder
  • 00:01:11
    we can use this rule to check if really
  • 00:01:13
    big numbers are multiples of a certain
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    number
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    for example if we wanted to check
  • 00:01:19
    whether 378
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    and 412 were multiples of
  • 00:01:25
    all we need to do is divide them both by
  • 00:01:27
    six
  • 00:01:30
    378 divided by six
  • 00:01:32
    is 63
  • 00:01:34
    so because 63 is a whole number
  • 00:01:38
    378 must be a multiple of 6.
  • 00:01:43
    412 divided by 6 though
  • 00:01:46
    is 68.6 recurring
  • 00:01:49
    which isn't a whole number
  • 00:01:51
    so 412 can't be a multiple of six
  • 00:01:56
    another way to think about the multiples
  • 00:01:58
    of a number
  • 00:02:00
    is to just keep on adding that same
  • 00:02:02
    number
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    so to find the multiples of 14
  • 00:02:07
    we could just keep adding 14.
  • 00:02:09
    so yeah 28 42 56
  • 00:02:14
    70 and so on
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    and all of these numbers that we get
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    would be the multiples of 14.
  • 00:02:24
    now the best way to understand factors
  • 00:02:27
    is to start with factor pairs
  • 00:02:30
    if we had the number 28
  • 00:02:32
    then its factor pairs
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    would be the pairs of whole numbers that
  • 00:02:37
    can be multiplied together to make
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    twenty-eight
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    so two times fourteen
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    four times seven
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    and one times twenty-eight
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    and if these six numbers that make up
  • 00:02:51
    these factor pairs that would be the
  • 00:02:53
    factors of 28
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    because they're all whole numbers that
  • 00:02:58
    can be multiplied by another whole
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    number to make 28.
  • 00:03:05
    another way to think about the factors
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    of a number
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    are all the numbers that divide into it
  • 00:03:11
    a whole number of times
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    for example 4
  • 00:03:16
    is a factor of 28
  • 00:03:18
    because 28 divided by 4 is 7
  • 00:03:22
    which is a whole number
  • 00:03:26
    whereas 5
  • 00:03:28
    isn't a factor
  • 00:03:29
    because 28 divided by 5 is 5.6
  • 00:03:34
    so 5 doesn't go into it a whole number
  • 00:03:37
    of times
  • 00:03:41
    if you want to quickly find all the
  • 00:03:43
    factors of a number
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    the best thing to do is write out all
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    the factors
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    starting with 1 times the number itself
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    so if we wanted to find all the factors
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    of 48
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    we'd start with 1 times 48
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    then do 2 times whatever factor is
  • 00:04:03
    needed to make 48
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    so 24
  • 00:04:07
    and so on
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    with 3 times 16
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    4 times 12
  • 00:04:12
    5 doesn't go into 48 so isn't a factor
  • 00:04:17
    then we have 6 times 8
  • 00:04:20
    7 also isn't a factor
  • 00:04:23
    and then we get to 8
  • 00:04:25
    which we've actually already covered in
  • 00:04:27
    six times eight
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    so we can stop here
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    and you know that our factors
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    in ascending order
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    are one
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    two
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    three
  • 00:04:38
    four
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    six
  • 00:04:40
    eight
  • 00:04:40
    12
  • 00:04:41
    16 24 and 48
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    so to find all the factors of 50
  • 00:04:51
    which do 1 times 50
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    2 times twenty-five
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    three doesn't go into fifty
  • 00:04:59
    four also doesn't work
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    five times ten
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    six
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    seven eight and nine don't work
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    and then we're at 10 which you've
  • 00:05:10
    already done
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    so the factors are just 1
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    2
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    5 10 25 and 50.
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    so to quickly sum everything up
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    if we took a number like 12
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    its multiples would be the bigger
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    numbers that it can multiply to
  • 00:05:32
    like 24 36 48 and so on
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    whereas its factors
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    are the numbers it can be divided into
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    like 1 2
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    3
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    4 6 and 12.
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    just make sure that you remember which
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    one is which
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    because it's really easy to get them the
  • 00:05:53
    wrong way around in the exam
  • 00:05:55
    and also remember that the number itself
  • 00:05:59
    counts as both a multiple and a factor
  • 00:06:02
    so 12 is in both of these lists
  • 00:06:09
    anyway that's everything for this video
  • 00:06:12
    so hope you enjoyed it and we'll see you
  • 00:06:14
    next time
  • 00:06:24
    you
タグ
  • mathematics
  • multiples
  • factors
  • division
  • multiplication
  • times tables
  • factor pairs