To solve the problem of determining the nature of the shaded numbers (multiples of 3) within the hundred chart, let's follow these steps.
1. Identify the multiples of 3 from 1 to 100:
- Multiples of 3 are numbers that can be expressed as [tex]\( \text{n} \times 3 \)[/tex] where [tex]\( \text{n} \)[/tex] is an integer.
- From 3 to 99, we list the multiples: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99.
2. Determine which of these multiples are prime numbers:
- Prime numbers are numbers greater than 1 that have no divisors other than 1 and themselves.
- Among the multiples of 3 listed above, the only prime number is 3. This is because all other multiples of 3 are not prime; they have at least 3 as a factor in addition to 1 and themselves.
3. Identify the composite numbers:
- Composite numbers are numbers greater than 1 that have more than two positive divisors.
- Therefore, all other multiples of 3 except 3 itself are composite numbers.
So, based on the analysis:
- The multiples of 3 in the range from 1 to 100 are: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99.
- Among these, the number 3 is prime.
- All other multiples are composite.
Therefore, the correct answer is:
(c) Some shaded numbers are prime and some are composite.
