Question

How many numbers are there from 200 to 700 which are divisible by 2,3 and 5 ?
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Answer 1

Answer:

the answer should be 9

Step-by-step explanation:

Since the required numbers are divisible by 2, 3 and 7, let

common difference, d=2×3×7=42

To find out the first number of the series, divide 300 by 42. We get remainder=6. So, the first number of the series is given by

a=300+(42-6)

=336

Similarly, to find the last number of the series, divide 700 by 42. We get remainder=28. So, the last number of the series is given by

l=700-28

=672

Let n be the number of numbers divisible by 42 from 300 to 700

Therefore,

l=a+(n-1)d

672=336+(n-1)42

336/42=n-1

n=8+1

Therefore, n=9