Question

A set m contains element all even number between 1 and 23 and all odd numbers 24 and 100. If all the elements of the set multiplied than how many trailing 0, resulting number will contain?

Answer 1

Answer:

Read Solution (Total 12)

( Answer will be 12 )

because the result trailing 0 occurs when one 2 and one 5 multiplied.

here we see the set M:

( 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 25, 35, 45, 55, 65, 75, 85, 95 )

after 22 I have taken only the term which contains factor of 5

now we find prime factor

2 = 2

4 = 2 * 2

6 = 2 * 3

8 = 2 * 2 * 2

10 = 2 * 5

12 = 2 * 2 * 3

14 = 2 * 7

16 = 2 * 2 * 2 * 2

18 = 2 * 3 * 3

20 = 2 * 2 * 5

22 = 2 * 11

25 = 5 * 5

35 = 5 * 7

45 = 5 * 9

55 = 5 * 11

65 = 5 * 13

75 = 5 * 5 * 3

85 = 5 * 17

95 = 5 * 19

here we find

total number of 5 is 12

and

total number of 2 is 19

and

we get total number of 5 * 2 pair is 12

so number of trailing zero will be 12

Answer 2

Answer: Number of trailing zero is 12 in the resulting number .

Concept : Number System

Given : A set m contains element all even number between 1 and 23 and

            all odd numbers 24 and 100. All the elements of the set are

            multiplied.

To Find : How many trailing 0 does the resulting number will contain.

Step-by-step explanation:

According to the question,

A set m contains element all even number between 1 and 23 and all odd numbers 24 and 100. All the elements of the set are multiplied and a resulting number is formed.

In the result trailing 0 occurs when one 2 and one 5 multiplied together .

The set m contains : { 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99 }

After 22,  we will take only the term which contains factors of 5 and will find the prime factors of the numbers.

⇒ 2 = 2

⇒ 4 = 2 * 2

⇒ 6 = 2 * 3

⇒ 8 = 2 * 2 * 2

⇒ 10 = 2 * 5

⇒ 12 = 2 * 2 * 3

⇒ 14 = 2 * 7

⇒ 16 = 2 * 2 * 2 * 2

⇒ 18 = 2 * 3 * 3

⇒ 20 = 2 * 2 * 5

⇒ 22 = 2 * 11

⇒ 25 = 5 * 5

⇒ 35 = 5 * 7

⇒ 45 = 5 * 3 * 3

⇒ 55 = 5 * 11

⇒ 65 = 5 * 13

⇒75 = 5 * 5 * 3

⇒ 85 = 5 * 17

⇒ 95 = 5 * 19

Total count of 5 is 12 and total count of 2 is 19.

So total number of 5 * 2 pair is 12

∴ The number of trailing zero will be 12.

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