A composite number is defined as a positive integer that has at least one positive divisor other than one or itself. In simpler terms, a composite number can be divided evenly by numbers other than just 1 and itself, meaning it has more than two factors.
Let’s analyze the two examples:
1. The number 7 x 11 x 13
Calculating this gives:
- 7 x 11 = 77
- 77 x 13 = 1001
So, the result is 1001. Now, let’s look at the factors of 1001:
- 1
- 7
- 11
- 13
- 77 (7 x 11)
- 91 (7 x 13)
- 143 (11 x 13)
- 1001 (1 x 1001)
The number 1001 has multiple divisors: 1, 7, 11, 13, 77, 91, 143, and 1001 itself, making it composite.
2. The number 7 x 6 x 5 x 4 x 3 x 2 x 15
Next, let’s evaluate this product:
- 7 x 6 = 42
- 42 x 5 = 210
- 210 x 4 = 840
- 840 x 3 = 2520
- 2520 x 2 = 5040
- 5040 x 15 = 75600
The result is 75600. Now we must consider its factors:
- 1
- 2
- 3
- 4
- 5
- 6
- 7
- 10
- 12
- 14
- 15
- 20
- 21
- 28
- 30
- 35
- 42
- 60
- 70
- 84
- 105
- 126
- 140
- 180
- 210
- 252
- 300
- 420
- 630
- 756
- 1260
- 2520
- 5040
- 75600
The number 75600 has numerous divisors, including all combinations of its prime factors. Hence, it too is a composite number.
In conclusion, both numbers (1001 and 75600) contain more than two factors, fitting the definition of composite numbers.