Question

1. If 10^n divides 6^23 * 75^9 * 105^2, then
what is the largest value of n?
(a) 20
(b) 22
(c) 23
(d) 28​

Answer 1

answer : option (a) 20

explanation : 10ⁿ divides 6^23 × 75^9 × 105^2 , then we have to find largest value of n.

first resolve all the given terms into simpler form.

i.e., 6²³ = (2 × 3)²³ = 2²³ × 3²³

75^9 = (3 × 5 × 5)^9 = (3 × 5²)^9 = 3^9 × 5^18

105² = (3 × 5 × 7)² = 3² × 5² × 7²

now, 6²³ × 75^9 × 105² = 2²³ × 3²³ × 3^9 × 5^18 × 3² × 5² × 7²

= (2²³ × 5^(18 + 2) ) × 3^(23 + 9 + 2) × 7²

= (2²³ × 5^20 ) × 3³⁴ × 7²

= 10^20 × 2³ × 3³⁴ × 7²

now 10^20 × 2³ × 3³⁴ × 7² is divided by 10ⁿ. then, largest value of n = power of 10 = 20

hence, option (a) is correct.

Answer 2

Answer:

(a) 20

Step-by-step explanation:

If 10^n divides 6^23 * 75^9 * 105^2, then equals 20