Prime and Composite Numbers worksheet for students to practice identifying and factoring numbers.

Let’s solve this step by step.

We are given 5 numbers: 43, 45, 47, 53, and 55.
For each, we need to:
1. List all its factors (numbers that divide it evenly).
2. Decide if it is prime or composite.

Remember:
- A prime number has exactly two factors: 1 and itself.
- A composite number has more than two factors.

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1) Number: 43

Check which numbers divide 43 evenly.

Try dividing by 2 → 43 ÷ 2 = 21.5 → not whole
Try 3 → 4+3=7, not divisible by 3 → no
Try 5 → doesn’t end in 0 or 5 → no
Try 7 → 7×6=42, 7×7=49 → too big → no
Try 11 → 11×3=33, 11×4=44 → too big → no
Actually, 43 is only divisible by 1 and 43.

✔ Factors: 1, 43
→ Only two factors → Prime

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2) Number: 45

Ends in 5 → divisible by 5 → 45 ÷ 5 = 9
Also, 4+5=9 → divisible by 3 → 45 ÷ 3 = 15
And 45 ÷ 1 = 45, 45 ÷ 9 = 5, etc.

List all factor pairs:
1 × 45
3 × 15
5 × 9

So factors: 1, 3, 5, 9, 15, 45 → six factors!

✔ Factors: 1, 3, 5, 9, 15, 45
→ More than two → Composite

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3) Number: 47

Check divisibility:

Not even → not divisible by 2
4+7=11 → not divisible by 3
Doesn’t end in 0 or 5 → not divisible by 5
7×6=42, 7×7=49 → too big → not divisible by 7
11×4=44, 11×5=55 → too big → no
13×3=39, 13×4=52 → too big → no

Only divisible by 1 and 47.

✔ Factors: 1, 47
→ Two factors → Prime

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4) Number: 53

Same process:

Not even → not divisible by 2
5+3=8 → not divisible by 3
Doesn’t end in 0 or 5 → not divisible by 5
7×7=49, 7×8=56 → too big → no
11×4=44, 11×5=55 → too big → no
13×4=52, 13×5=65 → too big → no

Only divisible by 1 and 53.

✔ Factors: 1, 53
→ Two factors → Prime

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5) Number: 55

Ends in 5 → divisible by 5 → 55 ÷ 5 = 11
Also, 55 ÷ 1 = 55, 55 ÷ 11 = 5

Factor pairs:
1 × 55
5 × 11

Factors: 1, 5, 11, 55 → four factors!

✔ Factors: 1, 5, 11, 55
→ More than two → Composite

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Now, the second part: Circle all the prime numbers from this list:

23, 31, 76, 55, 77,
25, 56, 47, 23, 80, 71,
37, 73, 51, 12, 89, 95

Let’s go one by one and check which are prime.

Recall: Prime = only divisible by 1 and itself.

Start:

- 23: Check divisors — not even, 2+3=5 not div by 3, not end in 5, 7×3=21, 7×4=28 → too big → only 1 and 23 → ✔ PRIME

- 31: Not even, 3+1=4 not div by 3, not end in 5, 7×4=28, 7×5=35 → too big → only 1 and 31 → ✔ PRIME

- 76: Even → divisible by 2 → ✘ COMPOSITE

- 55: Ends in 5 → divisible by 5 → 5×11 → ✘ COMPOSITE

- 77: 7×11 = 77 → ✘ COMPOSITE

- 25: 5×5 → ✘ COMPOSITE

- 56: Even → divisible by 2 → ✘ COMPOSITE

- 47: We already did above → ✔ PRIME

- 23: Already checked → ✔ PRIME (again)

- 80: Even → ✘ COMPOSITE

- 71: Let’s check — not even, 7+1=8 not div by 3, not end in 5, 7×10=70, 7×11=77 → too big, 11×6=66, 11×7=77 → too big → only 1 and 71 → ✔ PRIME

- 37: Not even, 3+7=10 not div by 3, not end in 5, 7×5=35, 7×6=42 → too big → only 1 and 37 → ✔ PRIME

- 73: Not even, 7+3=10 not div by 3, not end in 5, 7×10=70, 7×11=77 → too big, 11×6=66, 11×7=77 → too big → only 1 and 73 → ✔ PRIME

- 51: 5+1=6 → divisible by 3 → 51 ÷ 3 = 17 → so 3×17 → ✘ COMPOSITE

- 12: Even → divisible by 2 → ✘ COMPOSITE

- 89: Not even, 8+9=17 not div by 3, not end in 5, 7×12=84, 7×13=91 → too big, 11×8=88, 11×9=99 → too big, 13×6=78, 13×7=91 → too big → only 1 and 89 → ✔ PRIME

- 95: Ends in 5 → divisible by 5 → 5×19 → ✘ COMPOSITE

So primes in the box:
23, 31, 47, 23 (again), 71, 37, 73, 89

Note: 23 appears twice — we circle both instances.

Final Answer:

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Final Answer:

Part 1: Fill in the table

1) 43 → Factors: 1, 43 → Prime
2) 45 → Factors: 1, 3, 5, 9, 15, 45 → Composite
3) 47 → Factors: 1, 47 → Prime
4) 53 → Factors: 1, 53 → Prime
5) 55 → Factors: 1, 5, 11, 55 → Composite

Part 2: Circle all prime numbers in the box:

Circle these:
23, 31, 47, 23, 71, 37, 73, 89

*(Note: Do NOT circle 76, 55, 77, 25, 56, 80, 51, 12, 95 — they are composite.)*