Finding the Wrong Number in a Series

The question asks us to identify the number that does not fit the pattern in the given series: 3, 13, 43, 53, 63, 83.

To find the wrong number, we need to look for a rule or pattern that most numbers in the series follow. Let's examine the properties of each number:

• 3: This is a prime number. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.
• 13: This is a prime number. Its only positive divisors are 1 and 13.
• 43: This is a prime number. Its only positive divisors are 1 and 43.
• 53: This is a prime number. Its only positive divisors are 1 and 53.
• 63: Let's check if 63 is prime. We can try dividing it by small prime numbers:
  • 63 is not divisible by 2 (it's an odd number).
  • 63 is divisible by 3, since the sum of its digits (6 + 3 = 9) is divisible by 3. $63 \div 3 = 21$.
  Since 63 has divisors other than 1 and 63 (like 3 and 21), it is not a prime number. It is a composite number.
• 83: This is a prime number. Its only positive divisors are 1 and 83.

Upon analyzing the numbers, we see a pattern: most numbers in the series are prime numbers.

• 3 (Prime)
• 13 (Prime)
• 43 (Prime)
• 53 (Prime)
• 63 (Composite)
• 83 (Prime)

The number 63 is the only composite number in the series, while all other numbers (3, 13, 43, 53, and 83) are prime numbers. Therefore, 63 is the number that breaks the pattern and is the wrong number in the series based on the property of primality.

The final answer is 63.

Revision Table: Series Analysis

Let's summarize the properties of each number in the given series.

Additional Information: Prime and Composite Numbers

Understanding prime and composite numbers is key to solving problems like finding the wrong number in a series based on this property.

• Prime Numbers: A natural number greater than 1 that has exactly two distinct positive divisors: 1 and itself. Examples: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, etc.
• Composite Numbers: A natural number greater than 1 that has more than two distinct positive divisors. In other words, it can be formed by multiplying two smaller natural numbers. Examples: 4 ($2 \times 2$), 6 ($2 \times 3$), 8 ($2 \times 4$), 9 ($3 \times 3$), 10 ($2 \times 5$), 12 ($3 \times 4$), etc.
• The number 1 is neither prime nor composite.

Identifying prime and composite numbers often involves checking for divisibility by smaller prime numbers up to the square root of the number in question. In this case, for 63, checking divisibility by small primes like 2, 3, 5, 7 is sufficient to find factors other than 1 and 63.