Question

Jayne writes the integers from 1 to 2000 on a piece of paper. She erases all the multiples of 3, then all the multiples of 5, and so on, erasing all the multiples of each odd prime. How many numbers are left when she finishes?

Answer 1

Answer:

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Answer 2

Answer:

185 numbers

Step-by-step explanation:

$\red{\ggg} \pink{\underline{Question:-}}$

Jayne writes the integers from 1 to 2000 on a piece of paper. She erases all the multiples of 3, then all the multiples of 5, and so on, erasing all the multiples of each odd prime. How many numbers are left when she finishes?

$\red{\ggg} \pink{\underline{Solution:-}}$

Gayne writes integers from = 1 to 2000

After writing she erases all multiples of 3 and 5 and so on

They are so many odd primes from 1 to 2000

ODD PRIMES: The number divisible by 1 and itself

There are 303 odd prime numbers between 1 to 2000

First we should remove all 303 numbers from 2000

$\Rightarrow 2000-303=1697$

multiples of 5 up to 2000 = $\frac{2000}{5} =400$

$\Rightarrow 1697-400=1297$

Total multiples odd prime numbers up to 2000 = 1858 ( including 5 and odd prime numbers)

We should subtract 1858 from 2000

$\Rightarrow 2000-1858=142$

$\pink{185 \: \:numbers \: \:she \: \:left \:\:after \:\:finishing}$