Question

7. Find the greatest 3-digit number which is exactly divisible by 9, 15 and 18.
​

Answer 1

Answer:

:

3

is a factor for

9

,

15

and

18

, therefore the number must be divisible by

3

.

5

is a factor for

15

so the number must also be divisible by

5

. This means only 3-digit numbers ending in

0

or

5

can be considered.

2

is a factor of

18

therefore out of numbers ending in

0

and

5

we can now only consider numbers ending in

0

.

The first number to consider starting from 1000 and going backwards is

990

990

÷

9

=

110

990

÷

15

=

66

990

÷

18

=

55

The greatest 3-digit number exactly divisible by

9

,

15

and

18

is

990