Making a number: to make a number from the digits, we need to know about the Face Value and Place Value of digits:
Face value: the face value is the value of the digit in a number. We know that every number has a digit. Numbers may be of single- digit, two-digit, three-digit or more than three digits.
Example: 1,2,3,4….12,13 etc.
In number 1, the face value of digit 1 is 1
In number 13, the face value of one’s digit is 3 and ten’s digit is 1.
Place value: The place value of a digit is the value of the digit based on its place in the number.
Example: in the number 123, the digit 3 is at one’s place, so its place value is 1 and the digit 2 is at ten’s place, so its place value is 10 and digit 1 is at hundreds place, so its place value is 100.
Making a number: to make a number from the given digits, Multiply the Face Value of the digits with their Place Value and then add the results.
Example: suppose we need to make a number from the digits 2, 3 and 4 with 2 at One’s Place, 3 at Ten’s place and 4 at Hundred’s Place.
Multiply the Face Values with Place Values and then add altogether:
\(Face\ Value\ of\ 2\times Place\ Value\ of\ 2\)
\(+Face\ Value\ of\ 3\times Place\ Value\ of\ 3\)
\(+Face\ Value\ of\ 4\times Place\ Value\ of\ 4\)
\(=2\times1+3\times10+4\times100\)
\(=2+30+400\)
\(=432\)
So, the required number is 432
Natural number (N): a positive integer from 1 to infinity (\infty)
Example: 1,2,3,4,5,……so on.
Integer (Z): Any number form zero (0) to Negative infinity \((-\infty)\) or Positive infinity \(\left(+\infty\right)\), which is not a fraction or decimal number.
Examples: ……………-3, -2, -1, 0, 1, 2, 3……….
Example: 0,1,2,3,4,5……….
Rational numbers (Q): This is all the fractions where the top and bottom numbers are integers.
Examples: \(\frac{1}{2},\frac{5}{7},\frac{3}{4},\frac{7}{2},\frac{4}{3}\ etc.\)
Note: The denominator in a rational number, cannot be 0, but the numerator can be.
Real numbers (R): All the numbers including decimal numbers.
Example: 0.5, 0.75 2.35, 0.073, 0.3333, or 2.142857).
It also includes all the irrational numbers such as π, √2 etc.
Every real number corresponds to a point on the number line.
Prime number: A natural number which is divisible by 1 and number itself only, is known as prime number.
Or a number which has factors 1 and the number itself is called prime number.
Example: the number 2 is divisible by number 1 and 2 (itself) only, it has only two factors 1 and 2 (number itself), therefore it’s a prime number.
The number 5 has only two factors, 1 and 5 (number itself), therefore it’s a prime number.
Some other prime numbers are 3,7,11,13,17,19,23,29,31,37,41,43,47 etc.
The numbers mentioned above are divisible by the number 1 and number itself only.
Composite number: A positive integer which is not prime or a positive integer which can be formed by multiplying two smaller positive integers is called a composite number.
Example: number 4 can be written as \(2\ \times\ 2\), it has factors other than 1 and 4, therefore it’s a composite number.
Even number: any number which can be divided into group of 2 means any number divisible by 2 is called an even number such as 2,4,6,8,10,12,14,16,18,20 etc.
Odd Number: any number which can not be divided into group of 2 means any number not divisible by 2 is called an odd number such as 3,5,7,9,11,13,15,17,19 etc.
Factor: A number which divides the given number is called the factor of that number.
Example: the number 2 divides the number 4, therefore 2 is a factor of 4.
The number 3, divides the number 12, therefore 3 is a factor of 12.
Multiple: A number which is divisible by the given number is called the multiple of that number.
Example: the number 4 is divisible by 2 because it comes in 2’s table \((2\ \times\ 2=4)\), therefore 4 is a multiple of 2
The number 12 is divisible by 3 because it comes in 3’s table \((3\ \times\ 4=12)\), therefore 12 is a multiple of 3.
In the above example, we can see that number 3 completely divides number 12 i.e. remainder is zero, so we can say that:
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To learn about Factorization, click Here