Question

5. Write the prime factorisation of the following numbers in the exponential form:
(i) 24000
(ii) 12600
(iii) 14157​

Answer 1

To find : Prime factor of given number

Solution :

(i) 24000

= 24×1000

= (2×2×2×3)×(2×2×2×5×5×5)

rearranging factors, we get

= (2×2×2×2×2×2) × 3 × (5×5×5)

= 2⁶ × 3 × 5³

(ii) 12600

= 126 × 100

= 2×63 × (2×2×5×5)

= 2×(3×3×7) × (2×2×5×5)

rearranging factors , we get

= (2×2×2) × (3×3) × (5×5) × 7

= 2³ × 3² × 5² × 7

(iii) 14157

= 3×4719

= 3×(3×1573)

= 3×3 × (11×143)

= 3×3×11× (11×13)

rearranging factors, we get;

= (3×3)×(11×11)×(13)

= 3² × 11² × 13

Additional information :

• Prime number are those numbers which have only the factors, (1, and the number themselves)
• Composite number are those which have more than two factor