PSLEThere are two numbers. One is 3 times the other. They have exactly six common factors. Three of the common factors are 1, 7 and 49.
- 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, 7 and 49, the two numbers must be divisible by 1, 7 and 49.
Both numbers must be multiple of 49.
Multiples of 49: 49, 98, ...
49
= 1 x 49
= 7 x 7
Factors of 49: 1, 7, 49
However, 49 cannot be the smaller number because it has only 3 factors.
98
= 1 x 98
= 2 x 49
= 7 x 14
Factors of 98: 1, 2, 7, 14, 49, 98
As 98 has 6 factors and is divisible by 1, 7 and 49, it is the smaller number.
The other three factors are 2, 14 and 98.
(b)
The smaller number, 98, is the highest common factor.
Since the larger number is 3 times the other,
3 x 98 = 294
The two numbers are 98 and 294.
Answer(s): (a) 7, 14, 98; (b) 98, 294