how many integers from 1 to 1000 are divisible by 30 bt not 16
To find the number of integers from 1 to 1000 that are divisible by 30 but not by 16, you can use the following steps:
First, find the number of integers divisible by 30 in the range from 1 to 1000. To do this, divide 1000 by 30:
1000 ÷ 30 = 33.333...
Since we're looking for integers, there are 33 integers divisible by 30 in the range.
Next, find the number of integers divisible by both 30 and 16. To do this, find the least common multiple (LCM) of 30 and 16:
LCM(30, 16) = 240
Now, find the number of integers divisible by 240 in the range from 1 to 1000. To do this, divide 1000 by 240:
1000 ÷ 240 = 4.166...
Since we're looking for integers, there are 4 integers divisible by both 30 and 16 in the range.
Now, subtract the number of integers divisible by both 30 and 16 from the total number of integers divisible by 30:
33 (divisible by 30) - 4 (divisible by both 30 and 16) = 29
So, there are 29 integers from 1 to 1000 that are divisible by 30 but not by 16. The answer is 29.
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