Now we are able to Playing with numbers. You can make addition, subtractions, Multiplications and divisions with the Numbers.
Any number you multiply to get another number. The result that you get known as factor. Factor of a number is an exact divisor of that number.
We can say that a number is a multiple of each of its factors 1 is a factor of every number. every number is a factor of itself. every factor of a number is an exact divisor of that number.
The numbers other than 1 whose only factors are 1 and the number itself are called Prime numbers.
Numbers having more than two factors are called Composite numbers.
1 is neither a prime nor a composite number.
Even and Odd numbers
Even Number- The Number divided by 2 and the quotient will be 0 is known as Even Number
2 is the smallest prime number which is even.
Odd Number- The Number not divided by 2 and the quotient will not be 0 is known as odd Number.
Every prime number except 2 is odd.
If a number has 0 in the ones place then it is divisible by 10.
A number which has either 0 or 5 in its ones place is divisible by 5
A number is divisible by 2 if it has any of the digits 0, 2, 4, 6 or 8 in its ones place.
If the sum of the digits is a multiple of 3, then the number is divisible by 3.
A number is divisible by 2 and 3 both then it is divisible by 6 also.
A number with 3 or more digits is divisible by 4 if the number formed by its last two digits (i.e. ones and tens) is divisible by 4.
A number with 4 or more digits is divisible by 8, if the number formed by the last three digits is divisible by 8.
If the sum of the digits of a number is divisible by 9, then the number itself is divisible by 9.
Find the difference between the sum of the digits at odd places (from the right) and the sum of the digits at even places (from the right) of the number. If the difference is either 0 or divisible by 11, then the number is divisible by 11.
Two numbers having only 1 as a common factor are called co-prime numbers.
If a number is divisible by another number then it is divisible by each of the factors of that number.
If a number is divisible by two co-prime numbers then it is divisible by their product also.
If two given numbers are divisible by a number, then their sum is also divisible by that number.
If two given numbers are divisible by a number, then their difference is also divisible by that number.
The only factors 2 and 3 are prime numbers. Such a factorisation of a number is called a prime factorisation.
The Highest Common Factor (HCF) of two or more given numbers is the highest (or greatest) of their common factors.
It is also known as Greatest Common Divisor (GCD).
The Lowest Common Multiple (LCM) of two or more given numbers is the lowest (or smallest or least) of their common multiples.
A number of situations in which we make use of the concepts of HCF and LCM.