Must Know Facts of Numbers
• 1 is neither prime number nor composite.
• The lowest prime number is 2.
• 2 is also the only even prime number.
• The lowest odd prime number is 3.
• In the number system,
i) The number of one digits numbers are = 9.
ii) The number of two digits numbers are = 99 - 9 = 90.
iii) The number of three digits numbers are = 999 - 99 = 900.
iv) The number of four digits numbers are = 9999 - 999 = 9000.
Similarly, we can get the number of the numbers of further digits. To remember it easily we put as many as zeros after 9 so that the total number of digits including 9 is equal to the number of digits in required number. For example, if we have to find the number of 5 digit number, then we have to write four zeros after 9 i.e. 90000.
→ The difference between the largest and the smallest numbers of various digits-
Examples:
i. (The largest number of two digits) - (The smallest number of one digit.)
= 99 - 1 = 98.
ii. (The largest number of three digits) - (The smallest number of two digit.)
= 999 - 10 = 989.
iii. (The largest number of four digits) - (The smallest number of three digit.)
= 9999 - 100 = 9899.
Similarly, we can find out the difference between the numbers of further digits. To remember it easily we put as many 9 after 98 so that the total number of digits including 98 is equal to the number of digits of the larger number. For example if we have to find the difference between the largest number of six digits and smallest number of five digits, then we have to put 9999 after 98 i.e. 989999.
→ Numbers of prime numbers-
i) Between 1 and 25 = 9.
ii) Between 1 and 50 = 15.
iii) Between 1 and 100 = 25.
→ The remainder when a prime number P >= 5 is divided by 6 is 1 or 5. However a natural number when divided by 6 gives remainder of 1 or 5 the number need not be a prime.
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