14 Jan

Numbers

With the start of the New Year, your Preparation for SSC Combined Graduate Level exam must begin in the right earnest. For sure, many of you have already started working hard to improve your performance on the all important Quant section. Within Quant, dedicated effort is required to crack questions related to numerical ability (number system). Apart from this effort, you must also learn the special time saving shortcuts and tricks which will give you an edge over other exam aspirants.

Keeping this student need in mind, the centre for Best SSC Coaching in South Delhi has tried to demonstrate through a list of examples certain tricks that will help you find out the number of zeros at the end of a product of numbers or a factorial.

Finding Out the Number of Zeros

number of zeros

Question-I: How many zeros will be there at the end of 8 × 15 × 23 × 17 × 25 × 22?

Solution: 3

  • Zeroes are formed by a combination of 2×5.
  • 8 × 15 × 23 × 17 × 25 × 22 = (23) × (3×5) × (23) × (17) × (52) × (11×2).
  • So, here we can see that the maximum power of 2 is 4 & that of 5 is 3 (i.e. 24 & 53).
  • Therefore, the maximum number of pairs of (2 & 5) that can be formed is 3. Hence, the numbers of zeros will be 3.

Question-II: Find out the number of zeros at the end of 20 × 15 × 16 × 44 × 72 × 95 × 25.

Solution: 5

  • Zeroes are formed by a combination of 2×5.
  • 20 × 15 × 16 × 44 × 72 × 95 × 25 can be written as (22×5) × (3×5) × (24) × (22×11) × (23×32) × (5×19) × (52).
  • Over here, the maximum power of 2 is 11 and that of 5 is 5 (i.e. 211 & 55).
  • The number of zeros at the end of the given product will be 5 because the number of pairs of (2 & 5) that can be formed is 5.

Question-III: What will be the number of zeros at the end of 50!?

Solution: 12

50! = 1×2×3×4×5×6×7×……. × 50

We can clearly see, out here, that every second number is even (a multiple of 2) & every fifth number is a multiple of 5. This means the power of 5 will be less than the power of 2. Therefore, to find out the number of zeros in any factorial, we have to find only the power of 5 and not 2.

Here is a shortcut to find the number of zeroes at the end of 50!

Just divide this number 50 by 5 successively (again and again) & keep adding the quotient obtained from each step.

  • Step 1 – 50 / 5 = 10
  • Step 2 – 10 / 5 = 2

Adding these values we get 12 (10+2) as the number of zeros at the end of 50!

Question-IV: How many zeros are there at the end of 1000!?

Solution: 249

  • Step 1 – 1000 / 5 = 200
  • Step 2 – 200 / 5 = 40
  • Step 3 – 40 / 5 = 8
  • Step 4 – 8 / 5 = 1

Adding these values we get 249 (200+40+8+1) as the no. of zeros at the end of 1000!.

Question-V: Find out the number of zeros at the end of 160!.

Solution: 39

  • Step 1 – 160 / 5 = 32
  • Step 2 – 32 / 5 = 6
  • Step 3 – 6 / 5 = 1

Adding these values we get 39 (32+6+1) as the no. of zeros at the end of 160! = 39.

These tips and tricks are undoubtedly significant from the exam perspective. However, what matters even more is the practice that you put in along with attending classes at an SSC Coaching Institute. Only with consistent practice will you be able to recall these time saving tricks at the time of taking the exam.

Summary

This article presents highly relevant content for competitive exam preparation. You are encouraged to make full use of this content and even share it with other students. In case you have any doubt or confusion, pls. feel free to write to vidyagurudelhi@gmail.com. Your doubts and queries will be addressed by subject matter experts at Vidya Guru Institute.

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