If total number of even divisors of 1323000 which are divisible by 105 is 2k-10, then k is equal to

Question

If total number of even divisors of 1323000 which are divisible by 105 is 2k-10, then k is equal to (A) 5 (B) 6 (C) 7 (D) 8

Tardigrade Admin · Accepted Answer

1323000=23 ⋅ 33 ⋅ 53 ⋅ 72 105=3 ⋅ 5 ⋅ 7 ∴ Number of even divisors of 1323000 which are divisible by 105=3 × 3 × 3 × 2=54 ∴ 2 k -10=54 ⇒ 2 k =64 ⇒ k =6

Q. If total number of even divisors of 1323000 which are divisible by 105 is $2^{k} - 10$ , then $k$ is equal to

5

6

7

8

$1323000 = 2^{3} \cdot 3^{3} \cdot 5^{3} \cdot 7^{2}$
$105 = 3 \cdot 5 \cdot 7$
$∴$ Number of even divisors of 1323000 which are divisible by $105 = 3 \times 3 \times 3 \times 2 = 54$
$∴ 2^{k} - 10 = 54 \Rightarrow 2^{k} = 64 \Rightarrow k = 6$

Q. If total number of even divisors of 1323000 which are divisible by 105 is 2k−10, then k is equal to

5

6

7

8

1323000=23⋅33⋅53⋅72 105=3⋅5⋅7 ∴ Number of even divisors of 1323000 which are divisible by 105=3×3×3×2=54 ∴2k−10=54⇒2k=64⇒k=6

Q. If total number of even divisors of 1323000 which are divisible by 105 is $2^{k} - 10$ , then $k$ is equal to

$1323000 = 2^{3} \cdot 3^{3} \cdot 5^{3} \cdot 7^{2}$
$105 = 3 \cdot 5 \cdot 7$
$∴$ Number of even divisors of 1323000 which are divisible by $105 = 3 \times 3 \times 3 \times 2 = 54$
$∴ 2^{k} - 10 = 54 \Rightarrow 2^{k} = 64 \Rightarrow k = 6$