The factors of 98 are the numbers, that produce the result as 98 when two numbers are multiplied together. Consider an example, the factor pair of 53 is written as (1, 53) and (-1,-53). When we multiply the pair of negative factors, the result should give the original number, such as multiplying -1 × -53 then we get the number 53. Thus, we can consider both positive and negative factor pairs of 53. Factor pairs of the number 98 are the whole numbers which could be either positive or negative but not a fraction or decimal number. To find the factors of a number, 98, we will use the factorization method.

In the factorization method, first take the numbers, 1 and 98 as factors of 98 and proceed with finding the other pair of multiples of 98 which gives the results as an original number. To understand this method in a better way, read the article below to find factor 98 in pairs and also the division method to find the prime factors of 98 is discussed.

Table of Contents:

• What are the Factors of 98?
• Pair Factors of 98
• How to Calculate the Prime Factors of 98?
• Prime Factorization of 98
• Solved Examples
• FAQs

What are the Factors of 98?

The factors of 98 are the numbers that divide the number 98 without leaving the remainder. The factors of 98 are the number which is multiplied in pairs results in the original number 98. As the number 98 is a composite number, it has more than two factors. The list of factors of 98 is 1, 2, 7, 14, 49 and 98.

Pair Factors of 98

To find the pair factors of 98, multiply the two numbers in a pair to get the original number as 98, such numbers are as follows

If 1 × 98 = 98, then (1, 98) is a pair factor of 98.

Similarly,

2 × 49 = 98, (2, 49) is a pair factor of 98

7 × 14 = 98, (7, 14) is a pair factor of 98

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

To find the negative pair factors of 98, then proceed with the following steps

If -1 × -98 = 98, then (-1, -98) is a pair factor of 98.

Similarly,

-2 × -49 = 98, (-2, -49) is a pair factor of 98

-7 × -14 = 98, (-7, -14) is a pair factor of 98

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

How to calculate the Prime Factors of 98?

Learn the following steps to calculate the factors of 98.

• • First, write the number 98
  • Find the two numbers, which gives the result as 98 under the multiplication, say 7 and 14, such as 7 × 14 = 98
  • We know that 7 is a prime number that has only two factors, i.e., 1 and the number itself (1 and 7) which cannot be further factorized.  (i.e.) 7 = 7 × 1
  • But look at the number 14, which is a composite number but not a prime number and it can be further factorized. 14 can be factored as 7 x 2 x 1

• • Therefore, the factorization of 98 is written as 98 = 1 x 2 x 7 x 7

Finally, write down all the unique numbers that are obtained as factors.

Prime Factorization of 98

The number 98 is a composite and it should have prime factors. Now let us know how to calculate the prime factors of 98.

Step 1: The first step is to divide the number 98 with the smallest prime factor, say 2.

98 ÷ 2 = 49

Step 2: You will get a fractional number if you divide 49 by 2. Thus, continue with the next prime factor, 7.

49 ÷ 7 = 7

7 ÷ 7 = 1

Finally, we have received number 1 at the end of the division process. So that we cannot proceed further. So, the prime factors of 98 are written as 2 x 7 x 7 or 2 x 7², where 2, and 7 are the prime numbers.

It is possible to find the exact number of factors of a number 98 with the help of prime factorisation. The prime factor of the 98 is 2 x 7². The exponents in the prime factorisation are 1 and 2. Add the number 1 with the exponents and multiply it. (1+1)(2+1) = 2 x 3 = 6. Therefore, number 98 has 6 factors.

Examples

Example 1:

Find the common factors of 98 and 49

Solution:

The factors of 98 are 1, 2, 7, 14, 49 and 98.

The factors of 49 are 1, 7 and 49

Thus, the common factors of 98 and 49 are 1, 7 and 49

Example 2:

Find the common factors of 98 and 97.

Solution:

Factors of 98 = 1, 2, 7, 14, 49, 98

Factors of 97 = 1 and 97.

Therefore, the common factor of 98 and 97 is 1.

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