Question

how many integers between 1 and 567 are divisible by either 3 or 5?

Answer 1

105

210

315

420

525

This is the answer

Answer 2

Answer:

The number of integers that are divisible by either 3 or 5 is 265.

Step-by-step explanation:

We have to find a number that is divisible by either 3 or 5.

Now divide 567 by 3:

The quotient is 189 and the remainder is 0.

Now divide 567 by 5:

The quotient is 113 and the remainder is 2.

The L.C.M of 3 and 5 is 15

Now divide 567 by 15:

The quotient is 37 and the remainder is 12.

Thus the number of integers that are divisible by 3 is n(A) = 189.

Thus the number of integers that are divisible by 5 is n(B) = 113.

Thus the number of integers that are divisible by 15 is n(A ∩B) = 37.

We know that, n(A∪B) = n(A) + n(B) - n(A ∩B)

n(A∪B) = 189 + 113 - 37

n(A∪B) = 265

To learn more about divisibility, click on the below links:

https://brainly.in/question/6955261

https://brainly.in/question/13098038

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