High School

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------------------------------------------------ If the highest common factor (HCF) of two numbers is 29 and their sum is 174, what are the possible numbers?

A. 29 and 145
B. 58 and 116
C. 87 and 87
D. 29 and 145

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

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