PSLEThere 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.
- What are the other 3 common factors? Give your answers in ascending order. (Eg 1, 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 2 and 9.
Lowest common multiple of 2 and 9: 18
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.
The larger number is 2 times of the other.
Larger number
= 2 x 18
= 36
The two numbers are 18 and 36.
Answer(s): (a) 3, 6, 18; (b) 18, 36