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Question
How many integers from 1 to 1000 are divisible by 30 but not by 16 ?
29
31
32
38
ANSWER : 1
Descrption
<p style="margin-left:0px;">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:</p><p style="margin-left:0px;">First, find the number of integers divisible by 30 in the range from 1 to 1000. To do this, divide 1000 by 30:</p><p style="margin-left:0px;">1000 ÷ 30 = 33.333...</p><p style="margin-left:0px;">Since we're looking for integers, there are 33 integers divisible by 30 in the range.</p><p style="margin-left:0px;">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:</p><p style="margin-left:0px;">LCM(30, 16) = 240</p><p style="margin-left:0px;">Now, find the number of integers divisible by 240 in the range from 1 to 1000. To do this, divide 1000 by 240:</p><p style="margin-left:0px;">1000 ÷ 240 = 4.166...</p><p style="margin-left:0px;">Since we're looking for integers, there are 4 integers divisible by both 30 and 16 in the range.</p><p style="margin-left:0px;">Now, subtract the number of integers divisible by both 30 and 16 from the total number of integers divisible by 30:</p><p style="margin-left:0px;">33 (divisible by 30) - 4 (divisible by both 30 and 16) = 29</p><p style="margin-left:0px;">So, there are 29 integers from 1 to 1000 that are divisible by 30 but not by 16. The answer is 29.</p>
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