# Factors

## Factors:

• In mathematics, factors are those numbers which divide another number completely without leaving the remainder i.e. with zero remainder.
• Also, by multiplying the two or more factors we will get another number also.
• We have to note that, factors are only positive or negative whole numbers not fractions.
• The factors of any number are finite in number always.
• Factor of any number is less than that number or equal to that number always.
• Every number except 0 and 1, all has factors 1 and the number itself.

### For example:

• If we have to find the factors of 18.

Then, 18 = 6*3, 18 = 1*18

18= 2*3*3, 18 = 2*9

Thus, the factors of 18 are 1, 2, 3, 6, 9 and 18.

• And also, -1, -2, -3, -6, -9 and -18 all are the factors of 18.
• Because, when we take multiplication of two negative numbers then the answer will be positive.

Like, 18 = (-9)*(-2)

### Method of finding factors by Division method:

In this method, first we take the numbers below the given number and dividing by each number to the given number we will check the remainder. If the remainder is zero then that divisor is the factor of that number.

Only 1 and the number itself we have to not check.

For example:

• We find the factors of 8 by using division method.

So take the numbers less than 8 which are 2, 3, 4, 5, 6, and 7.

When we divide 8 by 2 then quotient is 4 and remainder is zero. Hence, 2 is the factor of 8.

Now, when we divide 8 by 3 then there will be no remainder zero with quotient as whole number. Hence, 3 is not the factor of 8.

When we divide 8 by 4 then quotient is 2 and remainder is zero. Hence, 4 is the factor of 8.

Similarly, when we divide 8 by 5, 6 and 7 we will not get the remainder zero with quotient as whole number. Hence, 5, 6 and 7 are not the factors of 8.

Finally, the factors of 8 are 1, 2, 4 and 8.

Also, the factors of 8 are -1, -2, -4 and -8.

• We find the factors of 15 by the same process.

We take numbers less than 15 which are 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, and 14;  and divide by it to 15 and we will check the remainder.

Then we found that, the numbers 1, 3, 5 and 15 divide 15 completely.

Hence, 1, 3, 5 and 15 are the factors of 15.

Also, -1, -3, -5 and -15 are factors of 15.

### Method of finding factors by multiplication:

In this method, we can write the given number in the form of multiplication of two number in all possible ways. And all these numbers expressed in the form of multiplication are the factors of given number.

For example:

• If we have to find factors of 8 by multiplication then we proceed as follows.

8 = 1*8, 8 = 2*4 also, 8 = (-1)*(-8), 8 = (-2)*(-4)

Thus, the factors of 8 are 1, 2, 4 and 8 also -1, -2, -4, and -8.

• If we have to find the factors of 15 by method of multiplication then first we write 15 in the form of multiplication of all possible numbers as follows.

15 = 1*15, 15 = 3*5

Hence, the factors of 15 are 1, -1, 3, -3, 5, -5, 15 and -15.

Updated: July 15, 2021 — 10:19 pm