To find the largest prime whose multiples should be crossed off before knowing that the remaining numbers in the table are prime, we can use the Sieve of Eratosthenes method.
We start by listing all the numbers from 2 up to 930. Then, we begin with the first number (2) and cross off all its multiples (4, 6, 8, 10, ...).
Moving on to the next uncrossed number, which is 3, we cross off all its multiples (6, 9, 12, 15, ...).
Continuing this process, we cross off all the multiples of the remaining uncrossed numbers in order. After completing the Sieve of Eratosthenes, the remaining uncrossed numbers are prime.
Therefore, to find the largest prime whose multiples should be crossed off, we need to determine the highest number that has not been crossed off when we finish the sieve.
Let's go through the process step by step:
1. Start by crossing off multiples of 2:
2, 4, 6, 8, 10, 12, 14, ..., 930 - All multiples of 2 are crossed off.
2. Move to the next uncrossed number, which is 3:
3, 6, 9, 12, 15, 18, ..., 930 - Cross off multiples of 3.
3. Move to the next uncrossed number, which is 5:
5, 10, 15, 20, ..., 930 - Cross off multiples of 5.
4. Continue with the next uncrossed number, which is 7:
7, 14, 21, 28, ..., 931 - Cross off multiples of 7.
5. Move to the next uncrossed number, which is 11:
11, 22, 33, ..., 935 - Cross off multiples of 11.
6. Continue this process until we reach the highest uncrossed number, which is less than or equal to the square root of 930. In this case, it is found to be 29.
So, the largest prime whose multiples we would cross off before knowing that the remaining numbers are prime using the Sieve of Eratosthenes is 29.
xopepe3030 06/16/2023 Mathematics High School answered • expert verified If you were using the Sieve of Eratosthenes to find all the prime numbers up to 930 , what is the largest prime whose multiples you would cross off before you knew that the remaining numbers in the table were prime?
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