how many number between 1 and 1200 both include are not divisible by any of the number 2,3,5
Answers
Answer:
There are 40 sets of 30 numbers from 1 to 1200 (1-30, 31-60, 61-90 ... ). From this I conclude that in each set there are 8 numbers that are not multiples of 2, 3 or 5, so there are 8 x 40 = 320 numbers altogether that are not multiples of 2, 3 or 5.
Step-by-step explanation:
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The number of numbers which are not divisible by 2, 3 and 5 in between 1 to 1200 is 320
Given:
Set of numbers from 1 to 1200
To find:
The number of numbers which are not divisible by 2, 3 and 5
Solution:
Given 1 to 1200 numbers
Numbers that are divisible by 2 = 2 to 1200
No of numbers divisible by 2 = 1200/2 = 600
Numbers that are divisible by 3 = 3 to 1200
No of numbers divisible by 3 = 1200/3 = 400
Numbers that are divisible by 5 = 5 to 1200
No of numbers divisible by 5 = 1200/5 = 240
Numbers that are divisible by 2 and 3 = 6 to 1200
No of numbers divisible by 2 and 3 = 1200/6 = 200
Numbers that are divisible by 3 and 5 = 15 to 1200
No of numbers divisible by 3 and 5 = 1200/15 = 80
Numbers that are divisible by 5 and 2 = 10 to 1200
No of numbers divisible by 5 and 2 = 1200/10 = 120
Numbers that are divisible by 2, 3 and 5 = 30 to 1200
No of numbers divisible by 2,3 and 5 = 1200/30 = 40
No of number which are not divisible by 2, 3 and 5
= 1200 - 600 - 400 - 240 + 200 + 80 + 120 - 40
= 1200 -1280 + 400
= 1600 - 1280 = 320
The number of numbers which are not divisible by 2, 3 and 5 is 320
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