Q. 25

Find the sum of all natural numbers from 1 and 100 which are divisible by 4 or 5.

Answer :

To Find: The sum of all natural numbers from 1 to 100 which are divisible by 4 or 5.


A number divisible by both 4 and 5 should be divisible by 20
which is the LCM of 4 and 5.


Sum of numbers divisible by 4 OR 5 = Sum of numbers divisible by 4 + Sum of numbers divisible by 5 - Sum of numbers divisible by both 4 and 5.


Sum of numbers divisible by 4 = 4 + 8 + 12 + …100
= 4(1 + 2 + 3 + …25)
Sum of numbers divisible by 5 = 5 + 10 + 15 + 20 + …100
= 5(1 + 2 + 3 + ..20)


Sum of numbers divisible by 20 = 20 + 40 + 60...100
= 20(1 + 2 + 3 + 4 + 5) = 20 × 15 = 300

Required sum = 1800 + 1050 - 300 = 2550


Sum of numbers which are divisible by 4 or 5 is 2550


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