Prime & Composite Numbers - Top Teacher - Free Printable

Let's solve this step by step based on the worksheet titled "Prime & Composite Numbers".

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🔹 Understanding the Concepts

- Prime Number: A number that has only two factors: 1 and itself.
- Example: 17 → only divisible by 1 and 17.
- Composite Number: A number with more than two factors.
- Example: 16 → divisible by 1, 2, 4, 8, 16.
- Note: 1 is neither prime nor composite because it has only one factor (itself).

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## ✔ Step 1: Highlight Prime Numbers on the Grid

We need to identify all prime numbers from 1 to 100.

Let’s go through the grid and list the prime numbers:

Primes between 1–100:
```
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
```

> These are the numbers you should highlight on the grid.

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Now let’s answer each question.

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❓ Question 2: List three composite numbers between 23 and 31.

Numbers between 23 and 31:
24, 25, 26, 27, 28, 29, 30

Check which are composite:
- 24 → divisible by 2, 3, 4, 6, 8, 12 → composite ✔
- 25 → divisible by 5 → 1, 5, 25 → composite ✔
- 26 → divisible by 2, 13 → composite ✔
- 27 → divisible by 3, 9 → composite ✔
- 28 → divisible by 2, 4, 7 → composite ✔
- 29 → prime ✘
- 30 → divisible by 2, 3, 5, 6, 10, 15 → composite ✔

So any three of these:
✔ 24, 25, 26 (or 27, 28, 30)

👉 Answer: 24, 25, 26

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❓ Question 3: List four prime numbers that are less than 15.

Primes less than 15:
- 2, 3, 5, 7, 11, 13

Choose any four:
👉 Answer: 2, 3, 5, 7

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❓ Question 4: Which decade has more composite numbers: the 70s or 80s?

Let’s list numbers in each decade and count composites.

#### 🔹 70s: 70 to 79
- 70 → composite (divisible by 2,5,7)
- 71 → prime
- 72 → composite
- 73 → prime
- 74 → composite
- 75 → composite (divisible by 3,5)
- 76 → composite
- 77 → composite (7×11)
- 78 → composite
- 79 → prime

Composites: 70, 72, 74, 75, 76, 77, 78 → 7 composites

#### 🔹 80s: 80 to 89
- 80 → composite
- 81 → composite (9×9)
- 82 → composite
- 83 → prime
- 84 → composite
- 85 → composite (5×17)
- 86 → composite
- 87 → composite (3×29)
- 88 → composite
- 89 → prime

Composites: 80, 81, 82, 84, 85, 86, 87, 88 → 8 composites

👉 So, 80s have more composite numbers.

✔ Answer: The 80s

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❓ Question 5: What is the last prime number on the grid?

The grid goes up to 100.

Look at the largest prime ≤ 100.

From earlier list:
97 is prime.
98 → even → not prime
99 → divisible by 3 → not prime
100 → not prime

So, 97 is the largest prime on the grid.

✔ Answer: 97

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❓ Question 6: Which number is composite, odd, between 40–60, and has 9 as a factor?

Let’s find numbers between 40 and 60 that are:
- Odd
- Composite
- Divisible by 9

Multiples of 9 between 40 and 60:
- 45 (9×5)
- 54 (9×6)

Now check:
- 45 → odd ✔, composite ✔ (factors: 1,3,5,9,15,45) → YES
- 54 → even ✘

So only 45 fits.

✔ Answer: 45

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❓ Question 7: Is 27 a prime number? YES / NO. List its factors.

27 → can be divided by:
- 1, 3, 9, 27 → more than two factors → composite

So, NO, it is not prime.

Factors: 1, 3, 9, 27

✔ Answer: NO, factors: 1, 3, 9, 27

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## ✔ Final Answers:

1. Highlight primes on the grid (as listed above).
2. Three composite numbers between 23 and 31: 24, 25, 26
3. Four prime numbers less than 15: 2, 3, 5, 7
4. Decade with more composite numbers: the 80s
5. Last prime number on the grid: 97
6. Number that is composite, odd, between 40–60, and has 9 as a factor: 45
7. Is 27 prime? NO, factors: 1, 3, 9, 27

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