Factors

FACTORS:

Factors are when two are more numbers are multiplied together  to get the product ,each number is called a Factor of the product.

                             (OR)

A Factor is a number that divides into another number exactly, without leaving a remainder.

Facts about Factors:

1)  A factor of a number is always be smaller than or equal to the number.

   Let the number be 12.Its factors are : 1,2,3,4,6, and 12.

   The factors : 1,2,3,4,6 < the number 12 . and other factor 12 = 12.

2) One,’1’ and the number itself are factors of any number.

  (i) Let the number be 9.Its factors are : 1,3,and 9.

  (ii) Let the number be 19. Its factors are : 1 and 19.

3) The number One,’1’ has only one factor – the number ‘1’ itself.

     All other numbers will have at least two factors.

 

Methods to find Factors:

There are two methods to find factors. They are:

(i)  Multiplication method.

(ii) Division method.

 

(i) Multiplication Method:

In this method, we find the numbers that can be multiplied with any other number to give the required product.

The Multiplicand and the Multiplier both are the factors, which when multiplied gives the required product.

 

1) 24.

Answer:

We need to find the numbers from 1 till 24 that can form the product 24.

FACTORS OF 24
1 * 24 = 24	2 * 12 = 24	3 * 8 = 24	4 * 6 = 24	5 * ?

Multiplicands: 1, 2, 3, 4.  Multipliers: 24, 12, 8, 6.

The numbers; 1, 2, 3, 4, 6, 8, 12, and 24 form the product 24. So, they are the factors of number 24.

The number ‘5’ can’t be multiplied with any number to give 24. So, it is not a factor of number 24.

The factors of number 24: 1, 2, 3, 4, 6, 8, 12 and 24.

 

2) 48.

Answer:

We need to find the numbers from 1 till 48 that can form the product 48.

FACTORS OF 48
1*48 =48	2 *24=48	3*16=48	4*12 =48	5 * ?	6*8=48

Multiplicands: 1, 2, 3, 4, 6. Multipliers: 48, 24, 16, 12, 8.    

The factors of number 48 are : 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.

 

3)  56.

Answer:

We need to find the numbers from 1 till 56 that can form the product 56.

FACTORS OF  56
1*56 =56	2*28=56	3*?=	4*14 =56	5 * ?=	6*?=	7*8=56

Multiplicands: 1 , 2, 4, 7 . Multipliers: 56, 28, 14, 8.

The factors of number 56 are : 1, 2, 4, 7, 8, 14, 28, and 56.

 

(ii) Division Method:

In this method, the factors are the divisors,  that divide the given number without leaving any remainder.

In division method, if the remainder is Zero then the factors are both Divisor and Quotient.

 

1) 32.

Answer:

We need to find the divisors from 1 till 32 that can divide 32 without leaving a remainder.

FACTORS OF  32
32÷1 = 32   R = 0	32÷2 = 16   R= 0	32÷3= 10    R = 2	32÷4 = 8   R = 0	32÷5 = 6   R= 2

Here, for the divisors: 3 and 5, the remainder is their i.e; 2. So, 3 and 5 are not factors of number 32. Other numbers 6,7,9,10, are also not factors as they leave  some remainder.

The divisors: 1, 2, 4 leaves remainder Zero with quotients: 32, 16, 8 for the number 32.

Thus, the factors of the number 32 are : 1, 2, 4, 8, 16, and 32.   

 

2) 64.

Answer:

We need to find the divisors from 1 till 64 that can divide 64 without leaving a  remainder.

FACTORS OF 64
64÷1 = 64, R = 0	64÷2 = 32, R = 0	64÷3 = 21, R =1	64÷4 = 16, R = 0	64÷5 = 12, R = 4	64÷6 = 10, R = 4	64÷7 = 9, R= 1	64÷8 = 8,  R=0

Divisors: 1, 2, 4, 8. Quotients: 64, 32, 16, 8.

The factors of the number 64 are:  1, 2, 4, 8, 16, 32, and 64.

 

3) 18.

Answer:

We need to find divisors from 1 till 18 that can divide 18 without leaving a remainder.

FACTORS OF 18
18÷1=18   R = 0	18÷2=9   R = 0	18÷3=6   R = 0	18÷4= 4   R = 2

 Divisors: 1, 2, 3. Quotients: 18, 9,6.

The factors of the number 18: 1, 2, 3, 6, 9, and 18.

The below table shows the Factors of a Number using Two methods:

S.NO	NUMBER	FACTORS OF  NUMBER
		Multiplication method:	Division method:
1	16	16 = 1*16 = 2* 8 =              4*4. Factors= 1,2,8,4,16 .	16÷1=16; 16÷2=8; 16÷4=4 . Factors = 1,24,8,16.
2	20	20 = 1*20 = 2*10 = 4*5. Factors= 1,2,4,5,10,20.	20÷1=20; 20÷2=10;  20÷4=5. Factors= 1,2,4,5,10,20.
3	45	45=1*45 = 3*15 = 5*9. Factors= 1,3,5,9,15,45.	45÷1=45; 45÷3=15; 45÷5=9. Factors= 1,3,5,9,15,45.