Question

DIG DEEPER Your friend says that all multiples of 12 are also multiples

of 3 and 6. Is your friend correct? Explain.

Answer 1

Answer: Yes

Step-by-step explanation: Yes, because since 3 goes into 12 successfully it should go into to any multiple of 12 since 3 is a factor of 12, the same for if multiples of 12 are also multiples of 6.

Answer 2

Correct

Explanation:

Well first let's define what a multiple of 12 would mean. A multiple of 12 can be divided by 12, or in other words "12" is a factor of that number.

This can be represented as:
`12n` where n is an integer.

if this is a multiple of 3 and 6, it means that it can be divided by 3 and 6.

`(12n)/(3) = 4n`, since n is an integer that means the quotient is an integer, thus any multiple of 12 will be a multiple of 4 since you can see it as:
`4*3*n` where 3n represents a multiple of 3 and then you just multiply it by 4. You can still divide this by 3 thus it's a multiple of 3

`(12n)/(6)=2n`, a similar thing happens hear since 12n which can represent any multiple of 12 is divisible by 6, than any multiple of 12 is a multiple of 6 because it has 6 as a factor