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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

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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