PSLEThere are two numbers. One is 5 times the other. They have exactly six common factors. Three of the common factors are 1, 5 and 25.
- 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, 5 and 25, the two numbers must be divisible by 1, 5 and 25.
Lowest common multiple of 5 and 25 = 25
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.
Multiples of 25: 25, 50 ...
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 common factors are 2, 10 and 50.
(b)
The smaller number, 50, the highest common factor.
The larger number is 5 times of the other.
Larger number
= 5 x 50
= 250
The two numbers are 50 and 250.
Answer(s): (a) 2, 10, 50; (b) 50, 250