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(Q). If p = 10! + 20! + 30! + 40! + ………… + 150!. then find the number of trailing zeros in pᵖ.
Solution:-

Number of trailing zeros in 

 

10! = 2 ⇒ 0020! = 4 ⇒000030! = 7 ⇒ 0000000150! = 37 ⇒ 00.........000

So number of trailing zeros in p = 2

So Let p = ( 00)Remaining any numbernow notice that( 00) ⇒ trailing zeros = 2×1 = 2( 00) ⇒ trailing zeros = 2×2 = 4( 00) ⇒ trailing zeros = 2×3 = 6( 00) ⇒ trailing zeros = 2×4 = 8( 00) ⇒ trailing zeros = 2×5 = 10( 00) ⇒ trailing zeros = 2×p = 2pp

Hence number of trailing zeros in pᵖ = 2p Answer