find the number of positive integers between 1 and 150 that are divisible by 2,3 and 7
Answers
76 numbers are available that are divisible by 2 between 1 and 150.
GIVEN: All positive integers.
TO FIND: Positive integers between 1 and 150 that are divisible by 2,3 and 7.
SOLUTION:
According to the question,
All positive integers are available from1 to 150.
The required positive integer should be divisible by 2,3 and 7.
After studying the series it can be said that,
2 is the first number divisible by 2.
148 is the last number divisible by 2.
Therefore,
An = 148 A1 = 2 d = 2
Using the formula of Arithmetic Progressions,
An = A1 + (n-1)d
148 = 2 + (n-1)2
148 + 2 = (n-1)2
150/2 = (n-1)
75 + 1 = n
76 = n
Therefore,
76 numbers are available between 1 and 150 that are divisible by 2.
The same process can be repeated for 3 and 7.
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