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Which of the following is the prime factorization of 120?
Which of the following lists of numbers is ordered from least on the left to greatest on the right?
Place one of the following numbers into the ones digit of the number 428, while moving the other digits so that the 4 is in the position of the tho...
ACT Aspire Math: Knowing (and Using) the Rules of Divisibility 13 Views
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Description:
Place one of the following numbers into the ones digit of the number 428, while moving the other digits so that the 4 is in the position of the thousands digit. What ones digit would make the number 428 divisible by 6 and 9?
Transcript
- 00:03
Okay Aspiring math people moving on another drill for you
- 00:07
Place one of the following numbers into the ones digit
- 00:10
of the number of four Twenty eight while moving the
- 00:12
other digits so that the four is in the position
- 00:16
of the thousands digit What one's digit would make the
Full Transcript
- 00:19
number for twenty eight divisible by six and by nine
- 00:27
Well the problem asked us to shift all digits to
- 00:30
the left and then tack on one more number to
- 00:32
the end But which number gets to join the group
- 00:35
here Well we can't just let any old number join
- 00:37
the club There are standards to solve this problem We
- 00:40
need to divide and conquer kind of there's division involved
- 00:43
anyway at least conquering that's So think of visibility rules
- 00:48
How does that work How do they work to be
- 00:50
divisible by six evenly a number must be divisible by
- 00:54
two and three and even number is divisible by two
- 00:58
duck and a number is divisible by three If the
- 01:01
digits add up to a multiple of three what we
- 01:04
mean by that is like four plus two plus a
- 01:07
That's fourteen is that divisible by three so much and
- 01:11
the rule for visibility by nine is similar If the
- 01:13
digits add up to a multiple of nine like they
- 01:17
some toe eighteen or twenty seven or thirty six like
- 01:20
that then it's all good We're also particularly fund of
- 01:23
this helpful little rule Nine is a multiple of three
- 01:25
So if a number is divisible by nine then of
- 01:28
course it must be divisible by three as well In
- 01:30
other words there's no need to check the rules for
- 01:33
both three and nine So if you have a niner
- 01:35
there the three work In short our number needs to
- 01:38
be divisible by both six and nine In other words
- 01:40
it needs to be even like in a c t
- 01:44
And the digits need to add up to a multiple
- 01:47
of nine Well the on ly answer that satisfies both
- 01:50
is four So uh that's c right there It gives
- 01:54
us four thousand two hundred eighty for if we adam
- 01:57
up for post to hiss six plus aids for eighteen
- 02:00
plus four there is eighteen eighteen of his wine nine
- 02:04
and then by definition by three as well So that's
- 02:07
it That's the answer It's see you'd stick up for
- 02:10
there in the thousands place and be done with this 00:02:12.578 --> [endTime] thing
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