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Prime and Composite Numbers

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Factor:
An exact divisor of a number is called its factor. When two or more numbers are multiplied the result obained is the product and the numbers multiplied are the facotrs of the product.

e.g. 1, 2, 3 and 6 are factors of number 6.

The number 1 is a factor of every number. Every number is a factor of itself. The factors of a number are either less than or equal to the number itself. All numbers have a finite number of factors.

Multiple:
The product of two numbers is called a multiple of each of the two numbers being multiplied.

A number is a multiple of all its factors. Every number is a multiple of 1 and of itself. There are infinite multiples of a number. Every multiple of a number is greater than or equal to that number.

Perfect number:
If the sum of the factors of a number is two times the number, then the number is called a perfect number.
e.g. Factors of 28 = 1, 2, 4, 7, 14, 28
Sum of the factors = 1 + 2 + 4 + 7 + 14 + 28 = 56
Two times of 28 = 2 x 28 = 56
∴ 28 is a perfect number.

Prime numbers:
Numbers that have only two factors i.e. 1 and the number itself are called prime numbers.
e.g. 5, 7, 11 etc.

Composite numbers:
Numbers that have more than two factors are called composite numbers. The number 1 is neither a prime number nor a composite number.
e.g. 4, 8, 10

Even numbers:
All the numbers with 0, 2, 4, 6 or 8 in the unit’s or one’s place are multiples of 2, and are called even numbers.

Odd numbers:
All numbers with 1, 3, 5, 7 or 9 in the unit’s or one’s place are called odd numbers.

The number 2 is the smallest prime number, and also the only prime number that is even. All prime numbers, except 2, are odd numbers. The sum of any two prime numbers, except with 2, is an even number.

Twin-primes:
Pairs of prime numbers with a difference of 2 are called twin-primes. 3 and 5; 5 and 7; 11 and 13 are examples of twin primes.

1 . Find the smallest 4 digit number.

Sol:

LCM of 18, 24 and 32:

18 = 2 x 3 x 3
24 = 2 x 2 x 2 x 3
32 = 2 x 2 x 2 x 2 x 2
LCM = 2 x 2 x 2 x 2 x

...

462

3 . Write the smallest 4 digit number and express it in terms of prime factors.

the smallest four digit niumber 1000.

1000= 2 3X5 3

4 . Largest number that divides 258 and 584 leaving remainder 6 and 8

Given that when 258 is divided by the number the remainder is 6
Similarly, when 584 is divided by the same number the remainder is 8...

5 . What is divisibility of 7

If you double the rightmost digit in a number and subtract it from the rest of the number, if the result is a multiple of 7 or if it is 0 th...

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