NCERT Class 8 Maths Chapter 2 – Prime Factorization Worksheet with Solutions (Power Play) Mock Test

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NCERT Class 8 Maths Chapter 2 – Prime Factorization Worksheet (Power Play)

NCERT Class 8 Maths Chapter 2 Mock Test


Practice Questions

Section A – Basic Level

  1. 72 = _______

  2. 180 = _______

  3. 225 = _______

  4. 128 = _______

  5. 250 = _______

Section B – Intermediate Level

  1. 392 = _______

  2. 500 = _______

  3. 900 = _______

  4. 1024 = _______

  5. 864 = _______

Section C – Advanced Level (Mixed Challenge)

  1. 1568 = _______

  2. 1875 = _______

  3. 2450 = _______

  4. 7200 = _______

  5. 9800 = _______

Bonus Question:

Find the HCF and LCM of 540 and 3600 using their prime factorization forms.

Tip / Self-Check:

✔ Always start dividing by the smallest prime number (2, then 3, then 5, etc.).
 ✔ When a number is no longer divisible by a prime, move to the next higher prime.
 ✔ Write repeated primes as powers for clean exponential form.

SOLUTION: Section A – Basic Level Solutions

(i) 72

Let’s divide by prime numbers step-by-step:

72 ÷ 2 = 36
 36 ÷ 2 = 18
 18 ÷ 2 = 9
 9 ÷ 3 = 3
 3 ÷ 3 = 1

Now count:

  • 2 appears 3 times → 2³

  • 3 appears 2 times → 3²

72 = 2³ × 3²

(ii) 180

180 ÷ 2 = 90
 90 ÷ 2 = 45
 45 ÷ 3 = 15
 15 ÷ 3 = 5
 5 ÷ 5 = 1

Now count:

  • 2 appears 2 times → 2²

  • 3 appears 2 times → 3²

  • 5 appears 1 time → 5¹

180 = 2² × 3² × 5

(iii) 225

225 ÷ 3 = 75
 75 ÷ 3 = 25
 25 ÷ 5 = 5
 5 ÷ 5 = 1

Now count:

  • 3 appears 2 times → 3²

  • 5 appears 2 times → 5²

 225 = 3² × 5²

(iv) 128

128 ÷ 2 = 64
 64 ÷ 2 = 32
 32 ÷ 2 = 16
 16 ÷ 2 = 8
 8 ÷ 2 = 4
 4 ÷ 2 = 2
 2 ÷ 2 = 1

Count:

  • 2 appears 7 times → 2⁷

 128 = 2⁷

(v) 250

250 ÷ 2 = 125
 125 ÷ 5 = 25
 25 ÷ 5 = 5
 5 ÷ 5 = 1

Count:

  • 2 appears 1 time → 2¹

  • 5 appears 3 times → 5³

 250 = 2 × 5³

Final Answers Summary Table

Number

Prime Factorization (Exponential Form)

72

2³ × 3²

180

2² × 3² × 5

225

3² × 5²

128

2⁷

250

2 × 5³


Section B – Intermediate Level Solutions

(vi) 392

Let’s divide by the smallest prime numbers:

392 ÷ 2 = 196
 196 ÷ 2 = 98
 98 ÷ 2 = 49
 49 ÷ 7 = 7
 7 ÷ 7 = 1

Count:

  • 2 appears 3 times → 2³

  • 7 appears 2 times → 7²

392 = 2³ × 7²

(vii) 500

500 ÷ 2 = 250
 250 ÷ 2 = 125
 125 ÷ 5 = 25
 25 ÷ 5 = 5
 5 ÷ 5 = 1

Count:

  • 2 appears 2 times → 2²

  • 5 appears 3 times → 5³

500 = 2² × 5³

(viii) 900

900 ÷ 2 = 450
 450 ÷ 2 = 225
 225 ÷ 3 = 75
 75 ÷ 3 = 25
 25 ÷ 5 = 5
 5 ÷ 5 = 1

Count:

  • 2 appears 2 times → 2²

  • 3 appears 2 times → 3²

  • 5 appears 2 times → 5²

900 = 2² × 3² × 5²

(ix) 1024

This number is a power of 2.

1024 ÷ 2 = 512
 512 ÷ 2 = 256
 256 ÷ 2 = 128
 128 ÷ 2 = 64
 64 ÷ 2 = 32
 32 ÷ 2 = 16
 16 ÷ 2 = 8
 8 ÷ 2 = 4
 4 ÷ 2 = 2
 2 ÷ 2 = 1

Count:

  • 2 appears 10 times → 2¹⁰

1024 = 2¹⁰

(x) 864

864 ÷ 2 = 432
 432 ÷ 2 = 216
 216 ÷ 2 = 108
 108 ÷ 2 = 54
 54 ÷ 2 = 27
 27 ÷ 3 = 9
 9 ÷ 3 = 3
 3 ÷ 3 = 1

Count:

  • 2 appears 5 times → 2⁵

  • 3 appears 3 times → 3³

864 = 2⁵ × 3³

Final Answers Summary Table

Number

Prime Factorization (Exponential Form)

392

2³ × 7²

500

2² × 5³

900

2² × 3² × 5²

1024

2¹⁰

864

2⁵ × 3³


Section C – Advanced Level Solutions

(xi) 1568

Let’s divide systematically by prime numbers:
 1568 ÷ 2 = 784
 784 ÷ 2 = 392
 392 ÷ 2 = 196
 196 ÷ 2 = 98
 98 ÷ 2 = 49
 49 ÷ 7 = 7
 7 ÷ 7 = 1

Count:

  • 2 appears 5 times → 2⁵

  • 7 appears 2 times → 7²

1568 = 2⁵ × 7²

(xii) 1875

1875 ÷ 3 = 625
 625 ÷ 5 = 125
 125 ÷ 5 = 25
 25 ÷ 5 = 5
 5 ÷ 5 = 1

Count:

  • 3 appears 1 time → 3¹

  • 5 appears 4 times → 5⁴

1875 = 3 × 5⁴

(xiii) 2450

2450 ÷ 2 = 1225
 1225 ÷ 5 = 245
 245 ÷ 5 = 49
 49 ÷ 7 = 7
 7 ÷ 7 = 1

Count:

  • 2 appears 1 time → 2¹

  • 5 appears 2 times → 5²

  • 7 appears 2 times → 7²

2450 = 2 × 5² × 7²

(xiv) 7200

7200 ÷ 2 = 3600
 3600 ÷ 2 = 1800
 1800 ÷ 2 = 900
 900 ÷ 2 = 450
 450 ÷ 2 = 225
 225 ÷ 3 = 75
 75 ÷ 3 = 25
 25 ÷ 5 = 5
 5 ÷ 5 = 1

Count:

  • 2 appears 5 times → 2⁵

  • 3 appears 2 times → 3²

  • 5 appears 2 times → 5²

7200 = 2⁵ × 3² × 5²

(xv) 9800

9800 ÷ 2 = 4900
 4900 ÷ 2 = 2450
 2450 ÷ 2 = 1225
 1225 ÷ 5 = 245
 245 ÷ 5 = 49
 49 ÷ 7 = 7
 7 ÷ 7 = 1

Count:

  • 2 appears 3 times → 2³

  • 5 appears 2 times → 5²

  • 7 appears 2 times → 7²

9800 = 2³ × 5² × 7²

Final Answers Summary Table

Number

Prime Factorization (Exponential Form)

1568

2⁵ × 7²

1875

3 × 5⁴

2450

2 × 5² × 7²

7200

2⁵ × 3² × 5²

9800

2³ × 5² × 7²

🧾 Bonus Question (HCF & LCM of 540 and 3600)

From earlier results:

  • 540 = 2² × 3³ × 5¹

  • 3600 = 2⁴ × 3² × 5²

HCF = product of lowest powers → 2² × 3² × 5¹ = 4 × 9 × 5 = 180
 LCM = product of highest powers → 2⁴ × 3³ × 5² = 16 × 27 × 25 = 10,800

HCF = 180, LCM = 10,800

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