Prime Factorisation Questions

Prime factorisation questions given here with solutions will help students understand the concept of prime factorisation and how to use the concept to solve various types of problems. Students must practice these questions to score well in their examinations.

Also read: How to find prime factors?

Prime Factorisation Questions with Solutions

Now that we understand what is meant by prime factorisation, let us practice prime factorisation by solving the following questions.

Question 1: Find the prime factorisation of the following:

(i) 284

(ii) 393

(iii) 7084

(iv) 5595

Solution:

(i) 278

∴ Prime Factorisation of 284 = 2 × 2 × 71

(ii) 393

(iii) 7084

∴ Prime factorisation of 7084 = 2 × 2 × 7 × 11 × 23.

(iv) 5595

∴ Prime factorisation of 5595 = 3 × 5 × 373.

Question 2: Find the prime factorisation of the following:

(i) 23356

(ii) 50034

(iii) 3487

(iv) 18720

Solution:

(i) 23356

∴ Prime Factorisation of 23356 = 2 × 2 × 5839

(ii) 50034

∴ Prime Factorisation of 23356 = 2 × 3 × 31 × 269

(iii) 3487

∴ Prime Factorisation of 23356 = 11 × 317

(iv) 18720

∴ Prime Factorisation of 23356 = 2 × 2 × 2 × 2 × 2 × 3 × 3 × 5 × 13 = 2⁵ × 3² × 5 × 13

Question 3: State ‘true’ or ‘false’ for the following:

(i) 177 is a prime number

(ii) 1 is a composite number

(iii) The prime factorisation of 252 is 2² × 3³ × 7.

(iv) 5 × 33 is the prime factorisation of 165.

Solution:

(i) 177 is a prime number. (False)

(ii) 1 is a composite number. (False)

(iii) The prime factorisation of 252 is 2² × 3³ × 7. (True)

(iv) 5 × 33 is the prime factorisation of 165. (False)

Question 4: List the common prime factors of 256 and 156.

Solution:

Prime factorisation of 256 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

Prime factorisation of 156 = 2 × 2 × 3 × 13

The common prime factor of 256 and 156 is 2.

Question 5: List the common factors of 152 and 76.

Solution:

Prime factorisation of 152 = 2 × 2 × 2 × 19

Prime factorisation of 76 = 2 × 2 × 19

The common prime factors of 152 and 76 are 2 and 19.

Also Read:

• HCF and LCM
• Fractions
• Factors and Multiples
• Prime Factorisation Calculator

Question 6: Find the highest common factor of 34, 42 and 58.

Solution:

Prime factorisation of 34 = 2 × 17

Prime factorisation of 42 = 2 × 3 × 7

Prime factorisation of 58 = 2 × 29

The highest common factor of 34, 42, and 58 is 2.

Question 7: Find the lowest common multiple of 45, 75, and 125.

Solution:

Prime factorisation of 45 = 3 × 3 × 5

Prime factorisation of 75 = 3 × 5 × 5

Prime factorisation of 125 = 5 × 5 × 5

Lowest common multiple of 45, 65 and 125 = 3 × 3 × 5 × 5 × 5 = 1125.

Question 8: Fill in the blank:

(i) 435 = 3 × ___ × ____.

(ii) 378 = 2 × __ × 3 × ___ × ____.

(iii) 1125 = 3^__ × 5^__.

Solution:

(i) 435 = 3 × 5 × 9.

(ii) 378 = 2 × 3 × 3 × 3 × 7.

(iii) 1125 = 3² × 5³.

Question 9: Find the prime factorisation of 118724.

Solution:

The prime factorisation of 118724 is 2 × 2 × 67 × 443.

Question 10: Verify:

Prime factorisation of 284 × Prime factorisation of 456 = Prime factorisation of (284 × 456)

Solution:

Prime factorisation of 284 = 2 × 2 × 71

Prime factorisation of 456 = 2 × 2 × 2 × 3 × 19

Prime factorisation of (283 × 456) = prime factorisation of 129504

= 2 × 2 × 2 × 2 × 2 × 3 × 19 × 71

Clearly,

Prime factorisation of 284 × Prime factorisation of 456 = Prime factorisation of (284 × 456).

Related Video on Common Factors

Practice Questions on Prime Factorisation

1. Find the prime factorisation of following:

(i) 2267

(ii) 450

(iii) 3487

(iv) 380

(v) 191

2. Find the common prime factors of the following:

(i) 25, 65, and 55

(ii) 134 and 345

(iii) 36, 48, and 58

3. Find the lowest common multiple of the following:

(i) 34 and 45

(ii) 45, 24, and 16

(iii) 32, 16, and 18.

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