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Halla el mayor número de niños entre los cuales se pueden repartir simultáneamente 32,48 y 56 panes, de manera que en cualquiera de los casos cada uno reciba la misma cantidad. ¿ cuántos panes recibirá cada niño?

Answer :

TaeKwonDoIsDead

Answer:

8 loaves

Step-by-step explanation:

Possible english translation:

Find the largest number of children among whom 32.48 and 56 loaves can be distributed simultaneously, so that in either case each receives the same amount. How many loaves will each child receive?

Solution:

The max amount each one will receive from either 32, 48, or 56 loaves would basically be the HCF (highest common factor) of the 3 numbers.

To get HCF of the 3 numbers given, we follow the rule below:

  • Get prime factorization of each number (express the number as product of primes by dividing
  • Then we take the smallest power of shared factor

We show this below:

32/2 = 16/2 = 8/2 = 4/2 = 2

So,

32 = [tex]2^5[/tex]

48/2 = 24/2 = 12/2 =6/2 = 3

So,

48 = [tex]2^4*3[/tex]

56/2 = 28/2 = 14/2 = 7

56 = [tex]2^3*7[/tex]

Common factor is only "2" (in all 3 numbers) and the lowest powered one is 2^3, so the HCF is 8

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