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.

 

Rounding Off Decimal Numbers.

ROUNDING OFF DECIMAL NUMBERS:

Rounding means making a number simplier but keeping its value close to what it was. The result is less accurate, but easier to use.

Rounding off of Decimal number is same as Rounding-off Whole numbers.

While Rounding off a decimal number ,we need to follow the steps same as in Rounding off  whole number .They are:

Step-1 : Underline the  digit in the given place to be rounded in the decimal number.

Step-2 : Circle the digit right to the underlined digit .

Step-3 : Comparision: The circled digit in the  decimal number is compared with number ‘ 5 ‘ always.

(i) Rounded Down : If the circled digit in the decimal number is smaller than

 ( < ) number ‘5’,then the decimal number is Rounded down.i.e; the underline digit in the given place remains the same.

(ii)  Rounded Up: If the circled digit in the decimal number is greater than or equals to ( ≥) number ‘5’,then the decimal number is Rounded up.i.e; the underlined digit in the given place is increased to number ‘1’.

i.e; we need to add number ‘1’ to the underlined digit.

Step-4: After Rounded-down or Rounded-up  , replace all the digits to the right of the given place with Zeros.

Note: If Round off to nearest place is not given, then we need to round off that decimal number to its greatest place value by following the above steps.

 

1) Round off : 249.267 to its nearest Hundredths place ?

Answer:

Step-1: Underline the digit in the given place (Hundredth) to be rounded in the given decimal number: 249.267 .

Step-2:Circle the digit right to the digit to be rounded. We need to circle the digit in the Thousandths place i.e: digit ‘7’ .

Step-3: Comparing the circled digit ‘7’  with number ‘5’.  7 > 5,  i.e; Rounded-Up case.Therefore, we add number’1’ to the underlined digit. i.e; 6 + 1 =7.

Step-4: Replace all the digits right of the Hundredth place  with Zero.

Thus the decimal number formed after rounded off to its nearest Hundredths place is : 249.270 = 249.27 .

 

2)  Round off : 17.95 nearest to its Tenths place?

Answer:

Step-1: Underline the digit in the given place (Tenths) to be rounded in the given decimal number: 17.95 = 17.95 .

Step-2:Circle the digit right to the digit to be rounded. We need to circle the digit in the Hundredths place i.e: digit ‘5’ .

Step-3: Comparing the circled digit ‘5’  with number ‘5’.  5 = 5,  i.e; Rounded-Up case.Therefore, we add number’1’ to the underlined digit. i.e; 9 + 1 =10.

Here, it’s a two digit number. Tens place digit : ‘1 ‘ is carry forward to whole number place Ones place.Digit ‘0’ is written in Tenths place.

Step-4: Replace all the digits right of the Tenth place  with Zero.

Thus the decimal number formed after rounded off to its nearest Tenths place is

= 18.00 = 18 , a whole number.

 

3) Round off : 3.3541 to its nearest Thousandths place.

Answer:

Step-1: Underline the digit in the given place (Hundredth) to be rounded in the given decimal number: 3.3541 .

Step-2:Circle the digit right to the digit to be rounded. We need to circle the digit in the TenThousandths place i.e: digit ‘1’ .

Step-3: Comparing the circled digit ‘1’  with number ‘5’.  1 < 5  i.e; Rounded-down  case. Therefore, we keep the digit to be rounded as it is.

Step-4: Replace all the digits right of the Thousandth place  with Zero.

Thus the decimal number formed after rounded off to its nearest Thousandths place is : 3.3540 = 3.354 .

 

The below table shows the Round-Off  decimal numbers to its nearest     

Tenths( 1/10), Hundredths( 1/100), Thousandths( 1/1000).

S.NO	NUMBER	ROUND OFF TO NEAREST PLACE
		1/ 10	1/ 100	1/ 1000
1	7.3485	7.3000    =  7.3	7.3500     = 7.35	7.3490  = 7.349
2	2.9868	3.0000   = 3	2.9900    =  2.99	2.9870   = 2.987
3	5.09187	5.10000    = 5.1	5.09000   = 5.09	5.09200  = 5.092
4	23.1381	23.1000  = 23.1	23.1400  = 23.14	23.1380 = 23.138
5	43.91441	43.90000 = 43.9	43.91000  = 43.91	43.91400 = 43.914