Question

How many times 2 will appear in the prime factorization of the product 1 × 2 × 3 × 4 × .... × 50 ?
1. 47
2. 48
3. 50
4. None of these

Answer 1

Correct Answer - Option 1 : 47

Calculation:

2 will appear in the prime factorization of the product 1 × 2 × 3 × 4 × . . . . × 50 is

⇒ 50 = 2 × 25

⇒ 25 = 2 × 12

⇒ 12 = 2 × 6

⇒ 6 = 2 × 3

⇒ 3 = 2 × 1

the sum of prime factorization of the product is

⇒ 25 + 12 + 6 + 3 + 1

⇒ 47

∴ Required times 2 will come is 47