what is the highest power of 30! that divides 3000! ?

JEE Mains 2015 Sample Questions › Fundamentals questions › what is the highest power of 30! that divides 3000! ?

what is the highest power of 30! that divides 3000! ?

#Mathematics #Fundamentals

UP 0 DOWN 0 0 5
Post on FacebookPost anonymously?

5 Answers

62

Lokesh Verma ·2010-05-12 09:38:06

the hint is that think of each prime factor of 30!

Then see what you can think..

Then post what you can and what you cannot.. then you get the remaining hint ;)

UP 0 DOWN 0
Post on FacebookPost anonymously?

1

archana anand ·2010-05-12 10:12:07

30!=2²⁶.3¹⁴.5⁷.7⁴.11².13².17.19.23.29
by same i mean only the power of given prime nos.

now find same for 3000!.

UP 0 DOWN 0
Post on FacebookPost anonymously?

62

Lokesh Verma ·2010-05-21 05:49:06

someone finishing it off?

UP 0 DOWN 0
Post on FacebookPost anonymously?

1

Aniket Ghosh Dastidar ·2010-05-24 03:06:08

Similarly 3000!=2²⁹⁹³.3¹⁴⁹⁸........29¹⁰⁶........2999.

Therefore for 3000! to be completely divisible by 30! all the prime factors till 29 in 3000! have to cancel out...

as power of 29 in 3000! is 106...the power of 29 in 30! in the denominator has to be 106.

Therefore the reqd power of 30! is 106

UP 0 DOWN 0
Post on FacebookPost anonymously?

62

Lokesh Verma ·2010-05-24 03:14:37

aniket.. I am not very sure about ur argument..

you need to justify that no other prime will create a trouble..

Finally you may or may not be correct..

UP 0 DOWN 0
Post on FacebookPost anonymously?

Your Answer

Basic Integral Calculus Operators Symbols Matrix Cases

√ √ || {} [] () → ~ ^ x x x → → ln log lg lim lim cos sin tan cot arcsin arccos arctan

∫ ∫ ∫ ∫ ∫ ∬ ∬ ∬ ∬ ∬ ∭ ∭ ∭ ∭ ∭ ⨌ ⨌ ⨌ ⨌ ⨌

∑ ∑ ∑ ∑ ∑ ∮ ∮ ∮ ∮ ∮ ∏ ∏ ∏ ∏ ∏ ∐ ∐ ∐ ∐ ∐

+ - × ÷ ± ∓ = ∪ ∩ ≠ ∼ ≈ ∅ ∀ ∃ ∈ ∋ ∝ ≤ ≥ ≃ ≅ ≡ < > ≪ ≫ ⊂ ∉ ⊃ ⊆ ⊇ ⇒ ⇐ ⇔ ⇒ ⇐ ⇔ ⇑ ⇓ ⇕ → ← ↔ → ← ↔ ↑ ↓ ↕ ↖ ↗ ↘ ↙ ↪ ↩ ⇀ ↼ ⇁ ↽

° ∂ ∞ α β γ δ θ λ μ ν ξ π ρ σ φ ω ε ƒ κ τ υ Γ Δ Λ Σ Π Ω