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Joined: 02 Jan 2020
Status:GRE Quant Tutor
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Schools: XLRI Jamshedpur, India - Class of 2014
GMAT 1: 700 Q51 V31
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Sieve of Eratosthenes : Prime numbers between 1 to 100
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23 Jul 2022, 01:39
23 Jul 2022, 01:39
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Hi All,
I have posted a video on YouTube to discuss about Sieve of Eratosthenes Method: To Find Prime Numbers between 1 to 100
Attached pdf of this Article as SPOILER at the top! Happy learning!
Following is Covered in the Video
- ¤ Sieve of Eratosthenes Method to find all prime numbers ≤ a number
¤ Find Prime numbers between 1 to 100
Sieve of Eratosthenes Method
Sieve of Eratosthenes Method is a method to find all the prime numbers ≤ a number.
Following are the steps involved in finding all the prime numbers ≤ n
STEP 1 : Cancel out 1 as it is not prime
STEP 2 : Find all the prime numbers from 2 to √𝑛
STEP 3 : Take each prime number from 2 to √𝑛 and cancel out all the multiples of these prime numbers except the number itself.
STEP 4 : Remaining numbers are prime numbers
Find Prime numbers between 1 to 100
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1.JPG [ 62.46 KiB | Viewed 1819 times ]
STEP 1 : Cancel out 1 as it is not prime
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2.JPG [ 62.63 KiB | Viewed 1776 times ]
STEP 2 : Find all the prime numbers from 2 to √𝑛
We need to find all the prime numbers from 2 to √100
=> Primes between 2 to 10, which are 2, 3, 5, 7 [ Watch this video to know about prime numbers ]
STEP 3 : Take each prime number from 2 to √𝑛 and cancel out all the multiples of these prime numbers except the number itself.
So, we will take all prime numbers 2, 3, 5 and 7 and cancel out their multiples, except the numbers 2, 3, 5, 7
STEP 3.1 : : Cancel out all multiples of 2 except 2. We will get :
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3.JPG [ 66.11 KiB | Viewed 1779 times ]
STEP 3.2 : : Cancel out all multiples of 3 except 3. We will get :
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4.JPG [ 67.17 KiB | Viewed 1773 times ]
STEP 3.3 : : Cancel out all multiples of 5 except 5. We will get :
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5.JPG [ 68.18 KiB | Viewed 1779 times ]
STEP 3.4 : : Cancel out all multiples of 7 except 7. We will get :
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6.JPG [ 70.42 KiB | Viewed 1781 times ]
STEP 4 : Remaining numbers are prime numbers
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7.JPG [ 26.4 KiB | Viewed 1787 times ]
There are 25 Prime Numbers between 1 and 100, which are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97
Hope it Helps!
gmatclubot
Sieve of Eratosthenes : Prime numbers between 1 to 100 [#permalink]
23 Jul 2022, 01:39
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