Question

Find the least number of 8 digits which is divisible by 566.
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Answer 1

Answer:

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Step-by-step explanation:

First number between 1 and 566 divisible by 3 is 3, and the last is 564. The numbers divisible by 3 are 3, 6, 9,…….564. Now 3= 3 x 1 and 564 = 3 x 188. So there are 188 numbers divisible by 3 between 1 and 566.

Again, the first number between 1 and 566 divisible by 5 is 5, and the last is 565. The numbers divisible by 5 are 5, 10, 15,…….565. Now 5= 5 x 1 and 565 = 5 x 113. So there are 113 numbers divisible by 5 between 1 and 566.

In the above two groups, we have included twice, the numbers which are divisible by their product. viz., 15. Hence, we have to remove the multiples of 15 once. Now, the first number between 1 and 566 divisible by 15 is 15, and the last is 555. The numbers divisible by 15 are 15, 30, 45,…….555. Now 15= 15 x 1 and 555 = 15 x 37. So there are 37 numbers divisible by 15 between 1 and 566.

Hence there are 188+113–37 = 264 integers between 1 and 566 which are divisible by 3 or 5.