Factors
Factor is a number which divides another number without leaving any remainder.
For Example:
The factors of 12 are 1, 2, 3, 4, 6, 12
We can write it as:
12 ÷ 1 = 12
12 ÷ 2 = 6
12 ÷ 3 = 4
12 ÷ 4 = 3
12 ÷ 6 = 2
12 ÷ 12 = 1
In the above cases we can see that it leaves no remainder.
Hence we can also write,
12 × 1 = 12 where 12 and 1 are the factors of 12
Again, 6 × 2 = 12 where 6 and 2 are the factors of 12
3 × 4 = 12 where 3 and 4 are the factors of 12
If we consider the number 51
Then 17 × 3 = 51 where 17 and 3 are the factors of 51
Again 51 ÷ 3 = 17 and 51 ÷ 17 = 3 leaving no remainder and hence 3 and 17 are the factors of 51
Important facts about factors :
I: If a divisor divides the dividend completely then we can say that the divisor is a factor of the dividend.
II: Suppose two or three numbers are multiplied to get the product then the numbers multiplied are called the factors of the number.
For Example:
7 × 5 × 3 = 105
Then 7, 5, 3 are the factors of 105
Similarly 11 × 2 × 3 = 66
Then, 11, 2, and 3 are the factors of 66
III: 1 is the factor of every number because 1 multiplied by any number is the number itself. Again any number divided by 1 is the number itself.
For Example:
1 × 32 = 32
Where 1 is the factor of 32
Again 32 ÷ 1 = 32
Hence, 1 is the factor of 32
IV: In case of prime numbers we have only two factor always that is1 and the number itself.
Here are few more examples on factors:
1. Find the factors of:
(a) 32
(b) 81
(c) 128
(d) 56
(e) 343
Solution:
(a) The factors of 32 are:
1, 2, 4, 8, 16, 32
(b) The factors of 81 are:
1, 3, 9, 27, 81
(c) The factors of 128 are:
1, 2, 4, , 16, 32, 64, 128
(d) The factors of 56 are :
1, 2, 4, 7, 14, 28, 56
(e) The factors of 343 are:
1, 7, 49, 343
2. Find the factors of:
(a) 256
(b) 72
(c) 36
(d) 54
(e) 112
Solution:
(a) The factors of 256 are:
1, 2, 4, 8, 16, 21, 64, 128, 256
(b) The factors of 72 are:
1, 2, 3, 4, 6, 8, 9, 12, 1, 24, 36, 72
(c) The factors of 36 are:
1, 2, 3, 4, 6, 9, 12, 18 36
(d) The factors of 54 are:
1, 2, 3, 6, 9, 18, 27, 54
(e) The factors of 112 are:
1, 2, 4, 7, 14, 28, 56, 112
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