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The number of zeros will be in last when 1 multiply 2 multiply 3 multiply 4 multiply 5 multiply 6 multiply 7 multiply 8 multiply 9 multiply 10 multiply 11 multiply 12 multiply 13 multiply 14 multiply 15 multiply 16 multiply 17 multiply 18 multiply 19 multiply 20?
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The number of zeros will be in last when 1 multiply 2 multiply 3 multi...
Understanding the Problem
To find the number of trailing zeros in the factorial of a number (in this case, 20!), we need to determine how many times 10 is a factor in the product. Since 10 is made up of 2 and 5, and there are usually more factors of 2 than 5 in factorials, we focus on counting the number of times 5 is a factor.
Counting the Factors of 5
To find the total number of factors of 5 in 20!, we can use the following method:
- Divide 20 by 5 and ignore the remainder.
- Continue dividing the quotient by 5 until it is less than 1.
Steps:
- 20 divided by 5 equals 4 (this counts how many multiples of 5 are there).
- Next, divide 4 by 5 equals 0 (this counts how many multiples of 25 are there, which contribute an extra factor of 5).
Calculating the Total
Now, we add the results:
- Total = 4 (from multiples of 5) + 0 (from multiples of 25) = 4.
Conclusion
Thus, the number of trailing zeros in 20! is 4. This means that when you multiply all integers from 1 to 20, the resulting product will end with 4 zeros.
Key Takeaway
- The number of trailing zeros in 20! is determined by the number of times 5 is a factor in the product.
- In this case, there are 4 trailing zeros in the multiplication of numbers from 1 to 20.
To find the number of trailing zeros in the factorial of a number (in this case, 20!), we need to determine how many times 10 is a factor in the product. Since 10 is made up of 2 and 5, and there are usually more factors of 2 than 5 in factorials, we focus on counting the number of times 5 is a factor.
Counting the Factors of 5
To find the total number of factors of 5 in 20!, we can use the following method:
- Divide 20 by 5 and ignore the remainder.
- Continue dividing the quotient by 5 until it is less than 1.
Steps:
- 20 divided by 5 equals 4 (this counts how many multiples of 5 are there).
- Next, divide 4 by 5 equals 0 (this counts how many multiples of 25 are there, which contribute an extra factor of 5).
Calculating the Total
Now, we add the results:
- Total = 4 (from multiples of 5) + 0 (from multiples of 25) = 4.
Conclusion
Thus, the number of trailing zeros in 20! is 4. This means that when you multiply all integers from 1 to 20, the resulting product will end with 4 zeros.
Key Takeaway
- The number of trailing zeros in 20! is determined by the number of times 5 is a factor in the product.
- In this case, there are 4 trailing zeros in the multiplication of numbers from 1 to 20.
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The number of zeros will be in last when 1 multiply 2 multiply 3 multiply 4 multiply 5 multiply 6 multiply 7 multiply 8 multiply 9 multiply 10 multiply 11 multiply 12 multiply 13 multiply 14 multiply 15 multiply 16 multiply 17 multiply 18 multiply 19 multiply 20?
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The number of zeros will be in last when 1 multiply 2 multiply 3 multiply 4 multiply 5 multiply 6 multiply 7 multiply 8 multiply 9 multiply 10 multiply 11 multiply 12 multiply 13 multiply 14 multiply 15 multiply 16 multiply 17 multiply 18 multiply 19 multiply 20? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about The number of zeros will be in last when 1 multiply 2 multiply 3 multiply 4 multiply 5 multiply 6 multiply 7 multiply 8 multiply 9 multiply 10 multiply 11 multiply 12 multiply 13 multiply 14 multiply 15 multiply 16 multiply 17 multiply 18 multiply 19 multiply 20? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of zeros will be in last when 1 multiply 2 multiply 3 multiply 4 multiply 5 multiply 6 multiply 7 multiply 8 multiply 9 multiply 10 multiply 11 multiply 12 multiply 13 multiply 14 multiply 15 multiply 16 multiply 17 multiply 18 multiply 19 multiply 20?.
The number of zeros will be in last when 1 multiply 2 multiply 3 multiply 4 multiply 5 multiply 6 multiply 7 multiply 8 multiply 9 multiply 10 multiply 11 multiply 12 multiply 13 multiply 14 multiply 15 multiply 16 multiply 17 multiply 18 multiply 19 multiply 20? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about The number of zeros will be in last when 1 multiply 2 multiply 3 multiply 4 multiply 5 multiply 6 multiply 7 multiply 8 multiply 9 multiply 10 multiply 11 multiply 12 multiply 13 multiply 14 multiply 15 multiply 16 multiply 17 multiply 18 multiply 19 multiply 20? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of zeros will be in last when 1 multiply 2 multiply 3 multiply 4 multiply 5 multiply 6 multiply 7 multiply 8 multiply 9 multiply 10 multiply 11 multiply 12 multiply 13 multiply 14 multiply 15 multiply 16 multiply 17 multiply 18 multiply 19 multiply 20?.
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