Determine the number of zeros at the right end of the numerals for the product. 1 x 2 x 3 × X 248 × 249 × 250 ... Your Answer:
Determine the number of zeros at the right end of the numerals for the product. 1 x 2 x 3 × X 248 × 249 × 250 ... Your Answer:
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Problem: Determine the number of zeros at the right end of the numerals for the product.**
Calculate the number of trailing zeros in the product:
\[1 \times 2 \times 3 \times \ldots \times 248 \times 249 \times 250\]
**Your Answer:** \_\_\_\_\_\_\_\_\_
---
To solve this problem, notice that a trailing zero is created by factors of 10, and each 10 is the product of a factor of 2 and a factor of 5. Therefore, the number of trailing zeros depends on how many times 10 is a factor in the product, which is determined by counting the number of pairs of 2s and 5s in the factorization of the product.
Key steps to consider:
1. Count the number of multiples of 5 in the sequence (they contribute one 5 each).
2. Count the multiples of 25, which contribute an additional factor of 5 each.
3. Continue with multiples of 125 if applicable.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd0ba01ff-d830-49b1-ab72-2b4d49e145df%2F5d50bc10-32fd-4831-b21b-1ef13237a9ee%2Fehdkgyi_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem: Determine the number of zeros at the right end of the numerals for the product.**
Calculate the number of trailing zeros in the product:
\[1 \times 2 \times 3 \times \ldots \times 248 \times 249 \times 250\]
**Your Answer:** \_\_\_\_\_\_\_\_\_
---
To solve this problem, notice that a trailing zero is created by factors of 10, and each 10 is the product of a factor of 2 and a factor of 5. Therefore, the number of trailing zeros depends on how many times 10 is a factor in the product, which is determined by counting the number of pairs of 2s and 5s in the factorization of the product.
Key steps to consider:
1. Count the number of multiples of 5 in the sequence (they contribute one 5 each).
2. Count the multiples of 25, which contribute an additional factor of 5 each.
3. Continue with multiples of 125 if applicable.
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