Answer :
Answer:
29 and 145
Step-by-step explanation:
We can find the possible numbers that have the HCF of 29 and the sum of 174 by this way:
Since both number have HCF of 29, then we can write:
- the 1st number as: 29a
- the 2nd number as: 29b
Next, since their sum equals to 174, then:
[tex]\begin{aligned}1st\ number+2nd\ number&=174\\29a+29b&=174\\29(a+b)&=174\\a+b&=6\end{aligned}[/tex]
The possibilities for a and b:
- 1 and 5
- 2 and 4
- 3 and 3
As their HCF equals to 29, which means there will be no other common factor between the 1st and 2nd number after both are divided by 29, therefore a and b have no common factor. From the 3 pairs above, only 1 and 5 meets this restrain.
Hence:
- 1st number = 29 × 1 = 29
- 2nd number = 29 × 5 = 145
