To solve this problem, we need to identify which numbers between 1 and 100 are
prime numbers.
Step-by-Step Reasoning:
1. Understand the Definition:
A prime number is a whole number greater than 1 that has exactly two factors: 1 and itself. This means it cannot be divided evenly by any other number.
*
1 is not a prime number (it only has one factor).
* Even numbers greater than 2 are not prime (they can be divided by 2).
* Numbers ending in 5 (greater than 5) are not prime (they can be divided by 5).
2. Process of Elimination (Sieve Method):
Let's go through the numbers from 1 to 100 and cross out the ones that are *not* prime (composite numbers).
*
Cross out 1: It is not prime.
*
Keep 2: It is the only even prime number.
*
Cross out all other even numbers: 4, 6, 8, 10, ..., 100.
*
Keep 3: It is prime.
*
Cross out multiples of 3: 9, 15, 21, 27, 33, 39, 45, 51, 57, 63, 69, 75, 81, 87, 93, 99.
*
Keep 5: It is prime.
*
Cross out multiples of 5 (ending in 5 or 0): We already crossed out the evens. Now cross out 15, 25, 35, 45, 55, 65, 75, 85, 95.
*
Keep 7: It is prime.
*
Cross out multiples of 7:
* $7 \times 7 = 49$
* $7 \times 11 = 77$
* $7 \times 13 = 91$
* (Other multiples like 14, 21, etc., were already crossed out as even numbers or multiples of 3).
*
Check remaining numbers: The next prime is 11. $11 \times 11 = 121$, which is bigger than 100. So, any number left standing that hasn't been crossed out is a prime number.
3. List the Remaining Prime Numbers:
*
1-10: 2, 3, 5, 7
*
11-20: 11, 13, 17, 19
*
21-30: 23, 29 (21, 25, 27 were crossed out)
*
31-40: 31, 37 (33, 35, 39 were crossed out)
*
41-50: 41, 43, 47 (45, 49 were crossed out)
*
51-60: 53, 59 (51, 55, 57 were crossed out)
*
61-70: 61, 67 (63, 65, 69 were crossed out)
*
71-80: 71, 73, 79 (75, 77 were crossed out)
*
81-90: 83, 89 (81, 85, 87 were crossed out)
*
91-100: 97 (91, 93, 95, 99 were crossed out)
4. Answer the Question "What are prime numbers?":
Based on our work, we can define them simply.
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Final Answer:
Tick these numbers on your chart:
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.
What are prime numbers?
Prime numbers are whole numbers greater than 1 that have only two factors: 1 and themselves. They cannot be divided evenly by any other number.
Parent Tip: Review the logic above to help your child master the concept of prime numbers worksheet.
