Divissssssssssssbillllllllty
How many natural numbers between 200 and 400 are there which are divisible by 4 or 5 or 8 or 10 ?
The answer is 79.
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2 solutions
I think that maybe you should use the word "multiple" instead of "factor" .
The number divisible by 8 will be divisible by 4 and the one divisible by 10 will be divisible by 5. Using A.P we can find out number of numbers divisible by4 and 5. which will contain numbers divisible by 8 and 10. then again applying A.P. we can calculate no of numbers divisible by 20. subtract this from earlier result Giving ans.
OVERRATED!!
N o o f n o s d i v i s i b l e b y 4 = 4 9 N o o f n o s d i v i s i b l e b y 5 = 3 9 T o t a l = 8 8 N o o f n o s d i v i s i b l e b y 2 0 = 9 S u b t r a c t i n g w e g e t a n s a s 7 9
The terms which are divisible by 8 should also be divisible by 4 and terms which are divisible by 10 must be divisible by 5 So we need to find all numbers between 200 and 400 (excluding both 200 and 400) which are divisible by 4 or 5.
Now, Total number of natural numbers between 200 and 400 divisible by 4 or 5 = Total number of factors of 4 + Total number of factors of 5 - Total number of factors of 20 Now , All numbers between 200 and 400 form an AP with common difference 4 and first term 204 and last term 396 let total number of terms be n Thus, an = a + (n-1)d 396 = 204 + (n-1)4 (n-1)4 = 192 n = 49 Again numbers divisible by 5 form an AP with common difference 5 and first term as 205 and last term as 395 Thus number of terms = ((an - a)/d) + 1 = ((395 - 205)/5)) + 1 = 39 Similarly for numbers of terms divisible by 20 are = ((380 - 220)/20) + 1 = 9 Thus total number of factors of 4 or 5 = 49 + 39 - 9 = 79