Question

How many integer numbers from 1 to 1000 are divisible by 2 or by 3?




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Answer 1

Step-by-step explanation:

First, there are precisely 500 integers between 1 and 1,000 which are divisible by 2. Second, there are 333 integers between 1 and 1,000 which are divisible by 3.

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Answer 2

Given

• numbers from 1 to 1000
• divisible by 2 or by 3

To find

• the number of integers present between the given number

Solution

we are provided with the numbers one and thousand and I asked to find the number of integers which are divisible by 2 and then by 3.

number of integers divisible by 2 present in between this range,

2, 4,6,.... ,998. this forms an AP

a = 2

d =2

l = 998

from the standard equation of arithmetic progression we can find the number of terms

an = a +( n-1)d

998 = 2 + (n-1)2

n-1 = 498

or, n = 499

the number of integers present in between the given range and he is divisible by 3

3,6,9,....,999 this is also an AP

a = 3

d = 3

l = 999

an = a +( n-1)d

999 = 3 + ( n-1)3

n-1 = 332

or, n = 333