Here are some basic rules to find out if the a number is a factor or not just by noting the number itself. I will suggest you to memorise these rules as they can be very handy in getting prime factors that are very essential to solve the problems of HCF, LCM or problems described in words. To refer the earlier posts on go to (click on the links will open in new window)

finding-number-of-factors-of-an-integer

tricks-and-ways-to-solve-the-hcf-and-lcm-problems

the rules are as follows:

1. If a is factor of b and b is factor of c then it can be said a is also a factor c. Infact, it is quite simple and obvious for example 2 is factor of 4 and 4 is factor of 8, then 2 is also a factor of 8.

2. If a is factor of both b & c, then it is also a factor of (b+c) or any sum of any multiple of b and c say (mb + nc) where m & n are positive integer

3. If a is factor of cd, such that there HCF of a and c is 1 i.e HCF(a,c) = 1 then a is factor of d as well

4. So that a and b are factor of each other, they must satisfyt a = b or a = -b

5. if number ab has a prime number as factor then the prime number is also a factor of a **OR** b

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