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How many trailing zeros will be there after the rightmost non-zero digit in the value of 25!?
- a)25
- b)8
- c)6
- d)5
- e)2
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
How many trailing zeros will be there after the rightmost non-zero dig...
25! means factorial 25 whose value = 25 × 24 × 23 × 22 × .... × 1
When a number that is a multiple of 5 is multiplied with an even number, it results in a trailing zero.
(Product of 5 and 2 is 10 and any number when multiplied with 10 or a power of 10 will have one or as many zeroes as the power of 10 with which it has been multiplied)
(Product of 5 and 2 is 10 and any number when multiplied with 10 or a power of 10 will have one or as many zeroes as the power of 10 with which it has been multiplied)
In 25!, the following numbers have 5 as their factor: 5, 10, 15, 20, and 25.
25 is the square of 5 and hence it has two 5s in it.
In toto, it is equivalent of having six 5s.
25 is the square of 5 and hence it has two 5s in it.
In toto, it is equivalent of having six 5s.
There are at least 6 even numbers in 25!
Hence, the number 25! will have 6 trailing zeroes in it.
Hence, the number 25! will have 6 trailing zeroes in it.
Choice C is the correct answer.
Most Upvoted Answer
How many trailing zeros will be there after the rightmost non-zero dig...
Trailing Zeros in Factorials
In order to find the number of trailing zeros in the value of 25!, we need to understand how trailing zeros are formed in factorials.
Formation of Trailing Zeros
- A trailing zero is formed when a multiple of 10 is produced in the factorial.
- Since 10 can be expressed as 2 * 5, we need to find the number of pairs of 2's and 5's in the factorial to determine the number of trailing zeros.
Counting the Number of 5's
- In the factorial of 25!, we need to count the number of multiples of 5 present.
- There are 5 multiples of 5 (5, 10, 15, 20, 25) in 25!.
- However, we need to consider the power of 5 in numbers like 25, where there are two factors of 5.
- So, we count 2 additional 5's from 25, making a total of 7 factors of 5 in 25!.
Number of Trailing Zeros
- Since there will always be more factors of 2 than 5 in factorials, we only need to count the number of factors of 5 to determine the number of trailing zeros.
- Therefore, the number of trailing zeros in 25! will be equal to the number of factors of 5, which is 6.
Therefore, the correct answer is option C) 6.
In order to find the number of trailing zeros in the value of 25!, we need to understand how trailing zeros are formed in factorials.
Formation of Trailing Zeros
- A trailing zero is formed when a multiple of 10 is produced in the factorial.
- Since 10 can be expressed as 2 * 5, we need to find the number of pairs of 2's and 5's in the factorial to determine the number of trailing zeros.
Counting the Number of 5's
- In the factorial of 25!, we need to count the number of multiples of 5 present.
- There are 5 multiples of 5 (5, 10, 15, 20, 25) in 25!.
- However, we need to consider the power of 5 in numbers like 25, where there are two factors of 5.
- So, we count 2 additional 5's from 25, making a total of 7 factors of 5 in 25!.
Number of Trailing Zeros
- Since there will always be more factors of 2 than 5 in factorials, we only need to count the number of factors of 5 to determine the number of trailing zeros.
- Therefore, the number of trailing zeros in 25! will be equal to the number of factors of 5, which is 6.
Therefore, the correct answer is option C) 6.
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How many trailing zeros will be there after the rightmost non-zero digit in the value of 25!?a)25b)8c)6d)5e)2Correct answer is option 'C'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about How many trailing zeros will be there after the rightmost non-zero digit in the value of 25!?a)25b)8c)6d)5e)2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for How many trailing zeros will be there after the rightmost non-zero digit in the value of 25!?a)25b)8c)6d)5e)2Correct answer is option 'C'. Can you explain this answer?.
How many trailing zeros will be there after the rightmost non-zero digit in the value of 25!?a)25b)8c)6d)5e)2Correct answer is option 'C'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about How many trailing zeros will be there after the rightmost non-zero digit in the value of 25!?a)25b)8c)6d)5e)2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for How many trailing zeros will be there after the rightmost non-zero digit in the value of 25!?a)25b)8c)6d)5e)2Correct answer is option 'C'. Can you explain this answer?.
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