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Dado el número N = 4752a, averigua qué valor ha de tomar "a" para que: a) N sea divisible por tres. b) N sea divisible por cinco. c) N sea divisible por 15. d) Cuando se divida N por 7 dé de resto 5.

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  1. Today, 00:29
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    I will answer it in English:

    a) We have te number N = 4752a

    if we want to divide it by 3, then the addition of all the digits must be a multiple of 3.

    Sum = 4 + 7 + 5 + 2 + a = 6 + 7 + 5 + a = 18 + a

    and 18 is a multiple of 3, then we can have, a = 0, a = 3, a = 6, a = 9

    b) A number is divisible by 5 if it ends on 5 or 0, so the possible values of a are 0 and 5.

    c) we know that 15*3 = 45

    then 15*3000 = 45000

    now we have:

    4752a - 45000 = 252a

    15*13 = 2520

    then we have that a must be equal to zero, and:

    15 * (13 + 3000) = 47520

    d) We want a number that when we divide it by 7, the surpass is 5.

    a number is divisible by 7 if the difference between the number without the units and the double of the units is 0 or a multiple of 7.

    in N = 4752x the unit is a, then we have:

    D = 4752 - 2*x

    now, let's choose a such we have a multiple of 7

    we know that 5746 is a multiple of 7, so we can choose x = 3 and get:

    D = 4752 - 2*3 = 5746

    So the number N = 47523 is a multiple of 7, and when we divide it by 7 we will have a surpass of 0.

    Then when we divide N + 5 by 7, we will have a surpass of 7.

    This is: N + 5 = 47528

    This means that the actual value of a that we need is 8.
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