The sum of two numbers is 204 and their HCF is 17. Find all the possible pairs of such numbers. Answer will be 119 but please explain with process
Answers
Step-by-step explanation:
It is given that the sum of the two numbers is 204, therefore,
x+y=204
Also 17 is their HCF, thus both numbers must be divisible by 17.
So, let x=17a and y=17b, then
17a+17b=204
⇒17(a+b)=204
⇒a+b=
17
204
⇒a+b=12
Therefore, required possible pair of values of x and y which are prime to each other are (1,11) and (5,7).
Thus, the required numbers are (17,187) and (85,119).
Hence, the number of possible pairs is 2.
Answer:
Since the HCF is 17, the number must be of the form 17a and 17b, where a and b are prime to each other.
Given, 17a + 17b = 204
=> a + b = 12
The possible pairs of numbers whose sum is 12 are 1, 11; 2, 10; 3, 9; 4, 8; 5, 7; 6, 6
The only pairs of numbers which are prime to each other are 1, 11; 12, 10; 3, 9; 4, 8; 5, 7; 6, 6
Therefore, the required pairs are 17 × 1 = 17
and 17 × 11 = 187
and 17 × 5 = 85
and 17 × 7 = 119.