Prime and Composite Numbers Worksheets - 15 Worksheets Library - Free Printable

I will solve the problem on this worksheet by identifying the factors for each number and determining if it is prime or composite. I will also circle all the prime numbers in the grid at the bottom.

Let me start by analyzing the first part of the worksheet, which asks for the factors and classification (prime or composite) for the numbers 43, 45, 47, 53, and 55.

Step 1: Analyze Number 43

- Factors: A factor is a number that divides another number evenly. For 43, I need to check which numbers divide it without a remainder.
- Since 43 is an odd number, it's not divisible by 2. Checking divisibility by 3: 4 + 3 = 7, which is not divisible by 3. It doesn't end in 0 or 5, so it's not divisible by 5. Checking higher primes like 7: 7 * 6 = 42, which is less than 43, and 7 * 7 = 49, which is greater than 43. Therefore, 43 has no other factors besides 1 and itself.
- Conclusion: The only factors of 43 are 1 and 43. Since it has exactly two distinct positive divisors, it is a prime number.

Step 2: Analyze Number 45

- Factors: 45 is an odd number but ends in 5, so it is divisible by 5. 45 ÷ 5 = 9. Also, 45 is divisible by 3 because 4 + 5 = 9, which is divisible by 3. 45 ÷ 3 = 15. We can also see that 45 = 9 * 5, and 9 = 3 * 3. So the factors are 1, 3, 5, 9, 15, and 45.
- Conclusion: Since 45 has more than two factors, it is a composite number.

Step 3: Analyze Number 47

- Factors: 47 is an odd number. Checking divisibility by 3: 4 + 7 = 11, not divisible by 3. Doesn't end in 0 or 5, so not divisible by 5. Checking 7: 7 * 6 = 42, 7 * 7 = 49 > 47. No other primes divide it.
- Conclusion: The only factors of 47 are 1 and 47. Therefore, it is a prime number.

Step 4: Analyze Number 53

- Factors: 53 is odd. Sum of digits 5 + 3 = 8, not divisible by 3. Doesn't end in 0 or 5. Checking 7: 7 * 7 = 49, 7 * 8 = 56 > 53. Checking 11: 11 * 4 = 44, 11 * 5 = 55 > 53. No other primes divide it.
- Conclusion: The only factors of 53 are 1 and 53. Therefore, it is a prime number.

Step 5: Analyze Number 55

- Factors: 55 ends in 5, so it is divisible by 5. 55 ÷ 5 = 11. So the factors are 1, 5, 11, and 55.
- Conclusion: Since 55 has more than two factors, it is a composite number.

Step 6: Circle All Prime Numbers in the Grid

The grid contains the following numbers:
23, 31, 76, 55, 77,
25, 56, 47, 23, 80, 71,
37, 73, 51, 12, 89, 95

I need to identify which of these are prime numbers.

- 23: Prime (factors: 1, 23)
- 31: Prime (factors: 1, 31)
- 76: Composite (even, divisible by 2)
- 55: Composite (divisible by 5 and 11)
- 77: Composite (7 * 11)
- 25: Composite (5 * 5)
- 56: Composite (even, divisible by 2)
- 47: Prime (factors: 1, 47)
- 23: Prime (already listed)
- 80: Composite (even, divisible by 2)
- 71: Prime (factors: 1, 71)
- 37: Prime (factors: 1, 37)
- 73: Prime (factors: 1, 73)
- 51: Composite (3 * 17)
- 12: Composite (even, divisible by 2)
- 89: Prime (factors: 1, 89)
- 95: Composite (divisible by 5 and 19)

The prime numbers to circle are: 23, 31, 47, 71, 37, 73, 89.

Final Answer:

Here is the completed worksheet:

Prime and Composite numbers

Write the factors for each number.
Then write if it is prime or composite.

| Number | Factor | Prime or Composite |
|--------|-------------------------|--------------------|
| 1) 43 | 1, 43 | Prime |
| 2) 45 | 1, 3, 5, 9, 15, 45 | Composite |
| 3) 47 | 1, 47 | Prime |
| 4) 53 | 1, 53 | Prime |
| 5) 55 | 1, 5, 11, 55 | Composite |

Circle all the prime numbers.

The prime numbers in the grid are: 23, 31, 47, 71, 37, 73, 89.