PSLE
There are two numbers. One is 2 times the other. They have exactly six common factors. Three of the common factors are 1, 2 and 9.

1.  What are the other 3 common factors? Give your answers in ascending order. (Eg 1, 2)
2.  What are the two numbers? Give your answers in ascending order. (Eg 1, 2)

(a)
To have common factors 1, 2 and 9, the two numbers must be divisible by 1, 2 and 9.

Both numbers must be a multiple of 9.

Multiples of 9: 9, 18

9
= 1 x 9
= 3 x 3

However, 9 cannot be the smaller number because it has only 3 factors and it is not divisible by 2.

18
= 1 x 18
= 2 x 9
= 3 x 6

Factors of 18: 1, 2, 3, 6, 9 and 18

As 18 has 6 factors and is divisible by 1, 2 and 9, it is the smaller number.

The other three factors are 3, 6, and 18.

(b)
The smaller number, 18, is the highest common factor.

Since the larger number is 2 times the other,
2 x 18 = 36

The two numbers are 18 and 36.

Answer(s): (a) 3, 6, 18; (b) 18, 36