Number of trailing zeros in a product important for CAT,E LITMUS,PLACEMENTS,GMAT,GRE/SSC CGL tier 2

In this post I would like to discuss some of the  fundamental ideas that can be used to solve number of trailing zeros in a product important for CAT,E LITMUS,PLACEMENTS,GMAT,GRE/SSC CGL tier 2. If you have just started your preparation you might find this article helpful.first of all we should have idea about number of trailing zeros trailing zeros are a sequence of 0s  after which no other digits follow.

think number 210 have one trailing zeros but have you ever thought why in this number only one trailing zero because 210 can be written as in form of prime factors

2 × 5 × 3 × 7 = 210  only one pair of 2 and 5 so  there is only there is only one zero at the end of the product  so number of trailing zeros depends upon number of pairs of 2’s and 5’s or We can say that for n number of zero’s at the end of the product we need exactly n combinations of “5 × 2 “. For example

Again 2 × 3 × 5 × 6 × 7 × 15 = 2 × 3 × 5 × 2 × 3 × 7 × 3 × 5

= 2 × 5× 2 × 5 × 3 × 3 × 3  × 7

= 100 × 189 = 18900

Thus there are two zeros because there are two combinations of “5 × 2 “.

Now, 1 × 2 × 3 × 4 × 5 × 6 × 7 × 8 × 9

= 1 × 2 × 3 × 2 × 2 × 5 × 2 × 3 × 7 × 2 × 2 × 2 × 3 × 3

= 1 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 5 × 3 × 3 × 3 × 3 ×  7

= 1 × 2⁷ × 5 × 3⁴ × 7

= 1 × 2⁶ × 2 × 5 × 3⁴ × 7

= 10 × 2⁶ × 3⁴ × 7

= 10 × 64 × 81 × 7

= 10 × 36288 = 362880

Thus there is only one zero at the end of the product since there is only one combination of 5 × 2.

Again 4 × 125 × 3 = 2 × 2 × 5 × 5 × 5 × 3

= 2² × 5³ × 3

=  2 × 5× 2 × 5    × 5 × 3

= 100 × 15 = 1500  Thus there are only two zeros at the end of the product since there is only one combination of “5 × 2”.

some CAT/ELITMUS /GRE /GMAT/SSC CGL MAINS  RELATED QUESTIONS

Find the number of trailing zeros in 5⁵×10¹⁰×15¹⁵×20²⁰×25²⁵×30³⁰

(a) 130         (b) 80                          (c) 100                         (d) None 

think why answer is  80  since there is only 80 combinations  of “5 × 2”.

Find the number of trailing zeros in 1¹×2²×3³×4⁴------------100¹⁰⁰

 (a) 1500                       (b) 1350                  (c) 1300                (d) 1050

click on this video for solution this question