Factors of 98

What are the Factors of 98

Factors of a number are the product of such numbers which completely divide the given number. Factors of a given number can be either positive or negative numbers. By multiplying the factors of a number we get the original number. For example 1, 2, 3, 6 are the factors of 6. On multiplying two or more numbers we get 6. Hence we have 2 x 3 = 6 or 1 x 6 = 6. On this page, we will study the factors of 98 definitions, what are the factors of 98, what is the prime factorization of 98, factor tree of 98, and examples. Factor pairs of the number 98 are the pairs of the whole numbers which could be either positive or negative but not a fraction or decimal number. Factorisation is the common method to find the factors of 98. Let us study the prime factorization of 98.

(image will be uploaded soon)


Factors of 98 Definition

The factors of a number are defined as the numbers which when multiplied will give the original number, by multiplying the two factors we get the result as the original number. The factors can be either positive or negative integers.


Factors of 98 are all the integers that can evenly divide the given number 98.

Now let us study how to calculate all factors of 98.


What are the Factors of 98?

According to the definition of factors of 98, we know that factors of 98 are all the positive or negative integers which divide the number 98 completely. So let us simply divide the number 98 by every number which completely divides 98 in ascending order till 98.


98 ÷ 1 = 98

98 ÷ 2 = 49

98 ÷ 3 = not divides completely

98 ÷ 4 = not divide completely

98 ÷ 5 = not divides completely

98 ÷ 6 = not divides completely

98 ÷ 7 = 14

98 ÷ 14 = 7

98 ÷ 49 = 2

98 ÷ 98 = 1 


So all factors of 98: 1, 2, 7, 14, 49, and 98.


We know that factors also include negative integers hence we can also have, 

list of negative factors of 98 : -1, -2, -7, -14, -49, and -98.


All Factors of 98 can be Listed as Follows


Positive Factors of 98

1, 2,, 7, 14, 49, and 98

Negative Factors of 98

-1, -2, -7, -14, -49, and -98.


Hence 98 have a total of 6 positive factors and 6 negative factors.


All Factor Pairs of 98

All Factor Pairs of 98 are combinations of two factors that when multiplied together give 98.


List of all the positive pair factors of 98

1 x 98 = 98; (1, 98)

2 x 49 = 98; (2, 49)

7 x 14 = 98; (7, 14)


So (1, 98), ( 2, 49), and (7, 14) are the positive pair factors of 98


As we know that Factors of 98 include negative integers too. 

List of all the negative pair factors of 98:

-1 x -98 = 98

-2 x -49 = 98

-7 x -14 = 98

So (-1, -98), ( -2, -49), and ( -7, -14)  are the negative pair factors of 98


Now we will study what is the prime factorization of 98.


What is the Prime Factorization of 98

According to the prime factor definition, we know that the prime factor of a number is the product of all the factors that are prime( a number that divides by itself and only one). Hence we can list the prime factors from the list of factors of 98.


Or the other way to find the prime factorization of 98 is by prime factorization or by factor tree.


Now let us study prime factors of 98 by division method.


Prime Factors of 98 by Division Method

To calculate the prime factors of 98 by division method, first, take the least prime number that is 2. Divide it by 2 until it is completely divisible by 2. If at a point it is not divisible by 2 take the next least prime number that is 3. Perform the same steps and move forward, till we get 1, as the quotient. Here is the stepwise method to calculate the prime factors of 98


Step 1: Divide 98 with 2

98 ÷ 2 = 49


Step 2: Again divide 32 with 2

49 ÷ 2 = 24.5

As it is not divisible by 2 completely let us take next prime number 3 


Step 3: Now divide 49 by 3

49 ÷ 3 = 16.33

It is also not divisible by 3. so let us check with other prime numbers. 


Step 4: Now 49 is  divisible by 7

49 ÷ 7 = 7


Step 5: Now 7 is again divisible by 7

7 ÷ 7 = 1

We get the quotient 1.


From the above steps, we get a prime factor of 98 as 2 x 7 x 7= 2 x 72

And also,

Here is the factor tree of 98.

(image will be uploaded soon)


Solved Examples

Example 1: Write down the factors of 16.

Solution:

16 ÷ 1 = 16

16 ÷ 2 = 8

16 ÷ 4 = 4

16 ÷ 8 = 2

16 ÷ 16 = 1

 Therefore the factors of 16 are 1, 2, 4, 8, and 16.


Example 2: Write down the factors of 68.

Solution:

68 ÷ 1 = 68

68 ÷ 2 = 34

68 ÷ 4 = 17

68 ÷ 17 = 4

68 ÷ 34 = 2

68 ÷ 68 = 1

Therefore the factors of 16 are 1, 2, 4, 17, 34 and 68.


Quiz time

  1. Find the factors for 81

  2. Find the factors for 56

FAQ (Frequently Asked Questions)

1. How to Calculate Factors of Large Numbers?

Answer: We can calculate factors of large numbers by the trial division method. We first try to divide the number by the smallest number such that it should completely divide the number. The result is again divided by the next number. This step is continued till we get the quotient as 1. At last, we will get all the factors of a given number. For example, let us factorize 100

  • 100 ÷ 2 = 50; first factor is 2

  • 100 ÷ 4 = 25;second factor is 4

  • 100 ÷ 5 = 20;third factor is 5

  • 100 ÷ 10 = 10;fourth factor is 10

  • 100 ÷ 20 = 5;fifth factor is 20

  • 100 ÷ 25 = 4;sixth factor is 25

  • 100 ÷ 50 = 2;seventh factor is 50

  • 100 ÷ 100 = 1;eighth factor is 100

So the factors of 100 are 2, 4, 5, 10, 20, 25, 50 and 100.

2. List the Important Facts of the Factors.

Answer:

Important Facts of Factors

  • A factor of any number is its exact divisor i.e it divides the given number exactly.

  • 1 is a common factor of every number.

  • Every factor of a number is always less than or equal to the original number.

  • The original number itself is the greatest factor.