# ACT Aspire Math: Knowing (and Using) the Rules of Divisibility

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?

ACT Aspire | Math |

ACT Aspire Math | The Number System |

Math | The Number System |

Product Type | ACT Aspire |

Test Prep | ACT Aspire ACT Aspire Math |

### Transcript

number for twenty eight divisible by six and by nine

Well the problem asked us to shift all digits to

the left and then tack on one more number to

the end But which number gets to join the group

here Well we can't just let any old number join

the club There are standards to solve this problem We

need to divide and conquer kind of there's division involved

anyway at least conquering that's So think of visibility rules

How does that work How do they work to be

divisible by six evenly a number must be divisible by

two and three and even number is divisible by two

duck and a number is divisible by three If the

digits add up to a multiple of three what we

mean by that is like four plus two plus a

That's fourteen is that divisible by three so much and

the rule for visibility by nine is similar If the

digits add up to a multiple of nine like they

some toe eighteen or twenty seven or thirty six like

that then it's all good We're also particularly fund of

this helpful little rule Nine is a multiple of three

So if a number is divisible by nine then of

course it must be divisible by three as well In

other words there's no need to check the rules for

both three and nine So if you have a niner

there the three work In short our number needs to

be divisible by both six and nine In other words

it needs to be even like in a c t

And the digits need to add up to a multiple

of nine Well the on ly answer that satisfies both

is four So uh that's c right there It gives

us four thousand two hundred eighty for if we adam

up for post to hiss six plus aids for eighteen

plus four there is eighteen eighteen of his wine nine

and then by definition by three as well So that's

it That's the answer It's see you'd stick up for

there in the thousands place and be done with this 00:02:12.578 --> [endTime] thing