Find whether 87 is a factor of 1748352 or number
The correct answer and explanation is:
Answer:
Yes, 87 is a factor of 1,748,352.
Explanation (300 words):
To determine whether 87 is a factor of 1,748,352, we need to check if dividing 1,748,352 by 87 gives a whole number (i.e., no remainder).
Step 1: Understanding Factors
A factor is a number that divides another number exactly, leaving no remainder. If we divide a number by another and the result is an integer, then the second number is a factor of the first.
Step 2: Division Check
Let’s divide: 1,748,35287=20,096\frac{1,748,352}{87} = 20,096
Since the result is a whole number (20,096), and there is no remainder, it confirms that 87 is a factor of 1,748,352.
Step 3: Verification
We can double-check by multiplying: 87×20,096=1,748,35287 \times 20,096 = 1,748,352
This confirms our previous result.
Step 4: Prime Factorization (Optional Insight)
Understanding factors can also be supported by examining prime factorizations:
- 87 can be factored into prime numbers as: 87=3×2987 = 3 \times 29
If both 3 and 29 are factors of 1,748,352, then 87 could be as well. This is a useful insight, especially for larger number factor checks.
Why This Matters
Factorization is a basic concept in number theory and is useful in many areas of mathematics and computer science, including cryptography and algebra. Determining if one number is a factor of another can help simplify problems, find least common multiples, or solve equations.
In practical terms, this tells us that 1,748,352 can be divided into 87 equal parts without any remainder, which can be useful in scenarios like distribution, programming loops, or understanding numerical relationships.
Conclusion:
Since 1,748,352 ÷ 87 = 20,096 exactly, 87 is indeed a factor of 1,748,352.