I will solve the problem presented in the image, which is a worksheet asking to list the prime factors for each number and determine if the number itself is prime.
First, I need to understand the instructions. The example shows that for the number 3, the prime factorization is "3" and since it's just one prime number, the answer is "Yes" (it is prime). For the number 9, the prime factorization is "3 x 3" and since it has more than one factor (even though they are the same), the answer is "No" (it is not prime).
I will now go through each of the 20 numbers on the worksheet, find their prime factors, and determine if they are prime numbers.
Step 1: Analyze Numbers 1-5
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1: The number 1 is not a prime number. By definition, a prime number must be greater than 1 and have exactly two distinct positive divisors: 1 and itself. Since 1 only has one divisor, it is not prime. It also does not have prime factors.
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2: The number 2 is a prime number. Its only prime factor is itself, 2.
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3: The number 3 is a prime number. Its only prime factor is itself, 3.
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4: The number 4 is not a prime number. Its prime factorization is 2 x 2.
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9: The number 9 is not a prime number. Its prime factorization is 3 x 3.
Step 2: Analyze Numbers 6-10
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6: The number 6 is not a prime number. Its prime factorization is 2 x 3.
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7: The number 7 is a prime number. Its only prime factor is itself, 7.
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8: The number 8 is not a prime number. Its prime factorization is 2 x 2 x 2.
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9: Already completed above.
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10: The number 10 is not a prime number. Its prime factorization is 2 x 5.
Step 3: Analyze Numbers 11-15
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11: The number 11 is a prime number. Its only prime factor is itself, 11.
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12: The number 12 is not a prime number. Its prime factorization is 2 x 2 x 3.
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13: The number 13 is a prime number. Its only prime factor is itself, 13.
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14: The number 14 is not a prime number. Its prime factorization is 2 x 7.
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15: The number 15 is not a prime number. Its prime factorization is 3 x 5.
Step 4: Analyze Numbers 16-20
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16: The number 16 is not a prime number. Its prime factorization is 2 x 2 x 2 x 2.
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17: The number 17 is a prime number. Its only prime factor is itself, 17.
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18: The number 18 is not a prime number. Its prime factorization is 2 x 3 x 3.
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19: The number 19 is a prime number. Its only prime factor is itself, 19.
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20: The number 20 is not a prime number. Its prime factorization is 2 x 2 x 5.
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Based on this analysis, here is the complete solution for the worksheet:
Which Numbers Are Prime Numbers?
For Example: 3 (Yes) 9 3 x 3 (No)
List the prime factors for each number. Is the number prime?
1. 1 =
(Not Prime) - No prime factors
2. 2 =
2 (Yes)
3. 3 =
3 (Yes)
4. 4 =
2 x 2 (No)
5. 5 =
5 (Yes)
6. 6 =
2 x 3 (No)
7. 7 =
7 (Yes)
8. 8 =
2 x 2 x 2 (No)
9. 9 =
3 x 3 (No)
10. 10 =
2 x 5 (No)
11. 11 =
11 (Yes)
12. 12 =
2 x 2 x 3 (No)
13. 13 =
13 (Yes)
14. 14 =
2 x 7 (No)
15. 15 =
3 x 5 (No)
16. 16 =
2 x 2 x 2 x 2 (No)
17. 17 =
17 (Yes)
18. 18 =
2 x 3 x 3 (No)
19. 19 =
19 (Yes)
20. 20 =
2 x 2 x 5 (No)
Parent Tip: Review the logic above to help your child master the concept of prime numbers 1 100 worksheet.
