Question

47,322 bulbs are to be packed in several boxes. Each box should contain"s equal numbers of bulbs and no bulb should be unpacked. Number of boxed used can be

Answer 1

Answer:

Number of boxes possible, any of the following,

1, 2, 3, 6, 9,11, 18, 22, 33, 66, 99, 198, 239, 478, 717, 1434, 2151, 2629, 4302, 5258, 7887, 15774, 23661, 47322

Step-by-step explanation:

To find the combinations number of boxes used we will first factorise the number 47322.

Factors of 47322 in terms of prime numbers,

47322 is divisible by 2, (Last digit of a  number divisible by 2)

47322 is divisible by 9 (4+7+3+2+2 = 18; divisible by 9)

47322 is divisible by 11 (4-7+3-2+2 = 0; divisible by 11)

∴ 47322 = 2 × 3 × 3 × 11 × 239  ..... (1)

Thus, number of boxes that can be packed without remainder are as follows;

239 or 2 or 3 or 11 or any multiple combination of these number from (1).

1, 2, 3, 6, 9,11, 18, 22, 33, 66, 99, 198, 239, 478, 717, 1434, 2151, 2629, 4302, 5258, 7887, 15774, 23661, 47322