Chap 3 Factors and Multiples

Chap 3

Factors and Multiples

Some Important facts:

1.    An exact divisor of a number is known as factor of the number.

2.    If any number a is completely divisible by number b then number a is said to be multiple of the number b.

3.    Every number is a factor and multiple of itself.

4.    Number 1 is factor of every number. Number 1 is neither a prime number nor a composite number.

5.    Number 2 is the only even prime number.

6.    Factors of each number are unique and there is no importance of their order.

7.    Divisibility Test  :  One number divisible by

(i)                    If a number having digits 0, 2, 4, 6, or 8 at units place is divisible by 2.

(ii)                  If a number having digits 0 or 5 at units place is divisible by 5.

(iii)                 If a number having 0 at units place is divisible by 10.

(iv)                 A given number is divisible by 4, if digits the number formed by their last two digit (i.e. digits at tens place and digit at unit place) is divisible by 4.

(v)                  A number is divisible by 8 if the number formed by its last three digits is divisible by 8.

(vi)                 A number is divisible by 3 if the sum of its digits is a multiple of 3.

(vii)                A number is divisible by 9 if the sum of its digits is a multiple of 9.

(viii)              A number is divisible by 11 if the difference of sum of its digit in odd places and the sum of its digits in even places (starting from the units’ places) is either 0 or a multiple of 11.

8.    Product of H.C.F. and L.C.M. of two numbers is equal to the product of two numbers.

9.    The common factor of two co-prime numbers is 1. Therefore H.C.F. of two prime and co-prime numbers is 1.

10.   The L.C.M. of two prime and co-prime numbers is equal to the product of numbers.

11.     We cannot write largest multiple of a number.

12. Prime numbers are countless and any prime number is not greatest prime number.

13. If a and b are two prime numbers and factor of any number c then a x b also a factor of number c.

14.  If any number a is a factor of both b and c, also b>c then ‘a’ is also a factor of b – c.

15.  If any number a is a factor of both b and c then ‘a’ is also ‘a’ factor of b + c.

16. L.C.M. of two or more than two numbers is that smallest number which is the common multiple off all the given numbers.