Question

The number of prime factors in (15)¹⁷ × (4)⁹ × (6)⁸ is:
1. 63
2. 60
3. 62
4. 68

Answer 1

Correct Answer - Option 4 : 68

Formula used:

a^m × aⁿ = a^{(m + n)}

Calculation:

(15)17 × (4)9 × (6)8

⇒ (3 × 5)17 × (2 × 2)9 × (3 × 2)8

⇒ 317 × 517 × 2⁹ × 29 × 3⁸ × 28

⇒ 3^{(17 + 8)} × 2⁽9 + 9 + 8) × 517 

⇒ 3²⁵ × 2²⁶ × 517 

Total factors = 25 + 26 + 17 = 68

∴ The number of prime factors in (15)17 × (4)9 × (6)8 is 68.

Prime Factor = Prime factor is finding which prime numbers multiply together to make the original number.