Question

How could you prove that a number is divisible by 16? Use the space below to test your hypothesis using the numbers 144 & 256. Explain your new rule.

Answer 1

We factor the number 16 into prime numbers to get their factors.

We do the same with any given number. Only if it has the same factor as 16 that numberwill be divisible by 16

Both numbers proposed (144&256) are divisible by 16

Explanation:

To prove it we need to factor the number 16 to get their expression in prime numbers:

16 2

8 2

4 2

2 2

1

16 is equal to
`2^(4)`

We have to factor a number and if their factor include
`2^(4)` or a higher power

then, they are divisible by 16

144 2

72 2

36 2

18 2

9 3

3 3

1

144 is queal to:
`2^4 . 3^2` as it does have
`2^4` It is divisible by 16

256 2

128 2

64 2

32 2

16 2

8 2

4 2

2 2

1

256 is equal to
`2^8` This contains
`2^4` as
`2^8 = 2^4 . 2^4`

therefore it is divisible by 16