PSLE
There are two numbers. Both are 2-digit numbers. One is 4 times the other. They have exactly five common factors. Three of the common factors are 1, 2 and 4.

1.  What are the other 2 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 4, the two numbers must be divisible by 1, 2 and 4.

Both numbers must be a multiple of 4.

Multiples of 4: 4, 8, ...

4 
= 1 x 4
= 2 x 2

Factors of 4: 1, 2 and 4

However, 4 cannot be the smaller number because it has only 3 factors.

The smaller number must have exactly five common factors.  So, it must be a square number.

16
= 1 x 16
= 2 x 8
= 4 x 4

Factors of 16: 1, 2, 4, 8, 16

So, 16 has 5 factors and is divisible by 1, 2 and 4, it is the smaller number.

The other two factors are 8 and 16.

(b)
The smaller number, 16, is the highest common factor. 

Since the larger number is 4 times the other,
4 x 16 = 64

The two numbers are 16 and 64.

Answer(s): (a) 8, 16; (b) 16, 64