Students identify and shade prime numbers in each set on this math worksheet.

Let's solve the problem step by step.

Task:

Shade the prime numbers in each set of numbers.

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What is a Prime Number?

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. In other words, it cannot be formed by multiplying two smaller natural numbers.

Examples: 2, 3, 5, 7, 11, 13, 17, 19, 23, ...

Note: Numbers like 4 (2×2), 6 (2×3), 8, 9 (3×3), etc., are not prime because they have factors other than 1 and themselves.

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We will go through each number in the image and determine whether it is prime or not.

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Set 1:

```
71 169 83 250 29 282 293
```

- 71: Check divisibility. Not divisible by 2,3,5,7. √71 ≈ 8.4 → check up to 7.
→ Prime
- 169: 13×13 = 169 → Not prime
- 83: Check up to √83 ≈ 9.1 → test 2,3,5,7 → none divide → Prime
- 250: Even → divisible by 2 → Not prime
- 29: Known prime → Prime
- 282: Even → divisible by 2 → Not prime
- 293: √293 ≈ 17.1 → check primes up to 17: 2,3,5,7,11,13,17 → none divide → Prime

✔ Primes in Set 1: 71, 83, 29, 293

---

Set 2:

```
18 101 55 211 187 125 227
```

- 18: Even → divisible by 2 → Not prime
- 101: √101 ≈ 10.05 → check 2,3,5,7 → none divide → Prime
- 55: Ends in 5 → divisible by 5 → Not prime
- 211: √211 ≈ 14.5 → check up to 13: 2,3,5,7,11,13 → none divide → Prime
- 187: 11×17 = 187 → Not prime
- 125: Ends in 5 → divisible by 5 → Not prime
- 227: √227 ≈ 15.1 → check up to 13: 2,3,5,7,11,13 → none divide → Prime

✔ Primes in Set 2: 101, 211, 227

---

Set 3:

```
169 229 113 73 257 81 237
```

- 169: 13×13 → Not prime
- 229: √229 ≈ 15.1 → check up to 13 → no divisors → Prime
- 113: √113 ≈ 10.6 → check 2,3,5,7 → none divide → Prime
- 73: Known prime → Prime
- 257: √257 ≈ 16.0 → check up to 13 → no divisors → Prime
- 81: 9×9 = 81 → Not prime
- 237: Sum of digits: 2+3+7=12 → divisible by 3 → 237 ÷ 3 = 79 → Not prime

✔ Primes in Set 3: 229, 113, 73, 257

---

Set 4:

```
51 27 97 281 230 241 195
```

- 51: 3×17 → Not prime
- 27: 3×9 → Not prime
- 97: √97 ≈ 9.8 → check up to 7 → no divisors → Prime
- 281: √281 ≈ 16.7 → check up to 13 → none divide → Prime
- 230: Even → Not prime
- 241: √241 ≈ 15.5 → check up to 13 → no divisors → Prime
- 195: Ends in 5 → divisible by 5 → Not prime

✔ Primes in Set 4: 97, 281, 241

---

Set 5:

```
283 299 173 151 163 181 197
```

- 283: √283 ≈ 16.8 → check up to 13 → no divisors → Prime
- 299: 13×23 = 299 → Not prime
- 173: √173 ≈ 13.5 → check up to 13 → no divisors → Prime
- 151: √151 ≈ 12.3 → check up to 11 → no divisors → Prime
- 163: √163 ≈ 12.7 → check up to 11 → no divisors → Prime
- 181: √181 ≈ 13.4 → check up to 13 → no divisors → Prime
- 197: √197 ≈ 14.0 → check up to 13 → no divisors → Prime

✔ Primes in Set 5: 283, 173, 151, 163, 181, 197

---

Set 6:

```
17 89 67 279 19 77 242
```

- 17: Prime → Prime
- 89: √89 ≈ 9.4 → check up to 7 → no divisors → Prime
- 67: Prime → Prime
- 279: Sum digits: 2+7+9=18 → divisible by 3 → 279÷3=93 → Not prime
- 19: Prime → Prime
- 77: 7×11 = 77 → Not prime
- 242: Even → Not prime

✔ Primes in Set 6: 17, 89, 67, 19

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✔ Final Answer: Shade the following numbers:

#### Set 1:
71, 83, 29, 293

#### Set 2:
101, 211, 227

#### Set 3:
229, 113, 73, 257

#### Set 4:
97, 281, 241

#### Set 5:
283, 173, 151, 163, 181, 197

#### Set 6:
17, 89, 67, 19

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🔍 Summary:

You should shade all the above numbers as they are prime.

> 💡 Tip: Use a pencil or highlighter to shade the boxes containing these numbers on the worksheet.

Let me know if you'd like this formatted for printing or as a checklist!