Question

Two numbers both greater than 29 have hcf 29 and 4147 the sum of the no is what

Answer 1

Answer:

As the HCF of the two numbers is 29, they are the multiple of 29.

Let the numbers are 29x and 29y .

We know that

Product of numbers = Product of LCM and HCF

Or, 29x × 29y = 4147 × 29

Or, xy = 143

Or, xy = 11 × 13, or 13 × 11, . . . . . . ( the only prime factors of 143 )

So, x = 11 or 13 and y = 11 or 13

And in either of the condition (x + y) = 24

Therefore,

29x + 29y = 29(x + y) = 29 × 24 = 696

Step-by-step explanation:

Answer 2

Step-by-step explanation:

Since the HCF of both the numbers is 29

let the numbers be 29a and 29b, where a and b are co-prime to each other.

Given, 29a × 29b = 29 × 4147 ⇔ ab = 143

The co-prime pairs (a, b) whose product = 143 are (1, 143) and (11, 13)

Since both the required numbers are greater than 29, the co-prime pair satisfying the condition is (11, 13).

Therefore the numbers are 29 × 11 and 29 × 13, i.e., 319 and 377.

∴ Sum of the numbers = 319 + 377 = 696.