Divisors and Factors
- Prime numbers are numbers having exactly two factors: 1 and the number itself. For example, the factors of 23 are 1 and 23 only. So, 23 is a prime number.
- Composite numbers are numbers having more than two factors. For example, the factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42. Since there are 8 factors of 42, it is a composite number.
- 1 is neither prime nor composite as it has exactly one factor.
- The smallest prime number is 2.
- The smallest even prime number is 2 and the smallest odd prime number is 3.
- All even numbers except 2 are composite.
- The pairs of prime numbers whose difference is 2 are known as twin primes. For example, 11 and 13 are twin primes.
- Closure Property of whole numbers:
- Whole numbers are closed under addition. For example, the sum of whole numbers 3 and 8 is 11 (3 + 8 = 11), which is again a whole number.
- Whole numbers are closed under multiplication. For example, the multiplication of whole numbers 4 and 7 is 28 (4 × 7 = 28), which is again a whole number.
- Whole numbers are not closed under subtraction. For example, 5 – 2 = 3 is a whole number, but 1 – 2 = –1 is not a whole number.
- Whole numbers are not closed under division. For example, 98…
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