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6 August, 05:10

The seven-digit number 1113A8B can be divided by 4, 5, and 9 What is the sum of the digits A and B?

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  1. 6 August, 06:03
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    4

    Step-by-step explanation:

    This seven-digit number can be divided by 4, 5 and 9.

    This means that 4, 5 and 9 are ALL factors.

    Find the least common multiply (LCM) of 4, 5 and 9.

    Multiples of 4: 4, 8, 12, 16, 20

    Multiples of 5: 5, 10, 15, 20

    Find a multiple of 9 that is also a multiple of 20. All multiples of 20 have the factors 4 and 5.

    9 X 20 = 180

    The seven-digit number must be a multiple of 180 to have the factor 4, 5 and 9. You can find the multiples of 180 until the number looks like 1113A8B, but there are better methods.

    All multiples of 180 end in the digit "0". Therefore B = 0.

    1113A80

    Since 9 is one of the factors, the rules for a number divisible for 3 apply. (9 is a multiple of 3).

    You know that a number is divisible by 3 when its digits add to a number divisible by 3.

    Find the sum of the digits:

    1+1+1+3+A+8+0 = A + 14

    A + 14 must be divisible by 3.

    Therefore, A has to be either 1, 4, or 7.

    If A = 1

    1113180 : 180 = 6184.333

    If A = 4

    1113480: 180 = 6186

    If A = 7

    1113780 : 180 = 6187.7

    A = 4 because that number is divisible by 180.

    Add A = 4 and B = 0.

    A + B

    = 4 + 0

    = 4

    The sum of digits A and B is 4.
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