Understanding Composite Numbers
Composite numbers are integers greater than one that have at least one divisor other than one and itself. This means they can be divided evenly by numbers other than just 1 and the number itself.
Analysis of 7×11×13 + 13
- Calculation:
- First, calculate 7×11×13. This equals 1001.
- Adding 13 gives us 1014.
- Divisibility:
- 1014 is even, as it ends in 4, meaning it is divisible by 2.
- Additionally, 1014 can be factored as 2 × 507. Since it has divisors other than 1 and itself, 1014 is a composite number.
Analysis of 7×6×5×3×2×1 + 5
- Calculation:
- First, calculate 7×6×5×3×2×1. This equals 5040.
- Adding 5 gives us 5045.
- Divisibility:
- 5045 ends with a 5, making it divisible by 5.
- We can also divide 5045 by 5 to get 1009. Since there are divisors other than 1 and 5045 (such as 5 and 1009), 5045 is also a composite number.
Conclusion
Both 1014 and 5045 are composite numbers due to their ability to be divided by integers other than 1 and themselves. This characteristic is essential in identifying composite numbers in mathematics.