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The number of prime factors in (21)22 × (15)8 × (6)12 is:
1. 84
2. 48
3. 42
4. 72

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Correct Answer - Option 1 : 84

Given:

(21)22 × (15)8 × (6)12

Formula used:

(ab)n = an × bn

Calculation:

(21)22 × (15)8 × (6)12

⇒ (3 × 7)22 × (3 × 5)8 × (2 × 3)12

⇒ 322 × 722 × 3× 58 × 212 × 312

⇒ 342 × 722 × 58 × 212 

Total prime factors = 42 + 22 + 8 +12 = 84

∴ The number of prime factors in (21)22 × (15)8 × (6)12  is 84.

Note:- Here total prime factors are asked. If we have to find the distinct prime numbers then our answer will be 4 (i.e. 2, 3, 5, 7)

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