PSLE
There are two numbers. One is 7 times the other. They have exactly six common factors. Three of the common factors are 1, 5 and 25.

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, 5 and 25, the two numbers must be divisible by 1, 5 and 25.

Both numbers must be a multiple of 25.

Multiples of 25: 25, 50, ...

25
= 1 x 25
= 5 x 5

Factors of 25: 1, 5, 25

However, 25 cannot be the smaller number because it has only 3 factors.

50
= 1 x 50
= 2 x 25
= 5 x 10

Factors of 50: 1, 2, 5, 10, 25, 50

As 50 has 6 factors and is divisible by 1, 5 and 25, it is the smaller number.

The other three factors are 2, 10 and 50.

(b)
The smaller number, 50, the highest common factor. 

Since the larger number is 7 times the other,
7 x 50 = 350

The two numbers are 50 and 350.

Answer(s): (a) 2, 10, 50; (b) 50, 350