The Factors of 98
What are the factors of 98?
Integers that divide 98 without leaving any remainder are known as factors of 98.
For example, 7 is a factor of 98 because when we divide 98 by 7, it leaves 14 as the quotient and 0 as the remainder. Here, the quotient is also a factor of 98.
So, to check if the number is a factor of 98 or not, divide 98 by that number and verify whether the remainder is zero or not.
Factor list of 98
So, the factors of 98 are 1, 2, 7, 14, 49, and 98.
The prime factors of 98
The number 98 is a composite number, that is, it has more than two factors. To find the prime factors, first we will divide the number 98 by its smallest prime factor, that is, 2.
98 ÷ 2 = 49
Now, divide by the next prime number, that is, 3, 5, 7, and so on.
49 ÷ 3 = 16.33, hence, 3 is not a factor.
49 ÷ 5 = 9.8, hence, 5 is not a factor.
So, divide by the next prime number, that is, 7.
49 ÷ 7 = 7
7 ÷ 7 = 1
So, the prime factorization of 98 = 2 × 7 × 7 or 2 × 7\(^2\).
This means that 2 and 7 are the prime factors of the number 98.
Read More:
The factor pairs of 98
The factor pairs of a number are two factors whose product is the number itself.
Example: (7, 14) is the factor pair of 98.
A factor pair can be a positive or a negative pair of numbers.
The positive factor pairs of 98
[Note: When two positive numbers are multiplied, the product is positive.]
Hence, the positive factor pairs of 98 are (1, 98), (2, 49), and (7, 14).
Rapid Recall
Factors of 98 are:
Solved Factors of 98 Examples
Example 1: Find the common factors of 98 and 100.
Solution:
Factors of 98 = 1, 2, 7, 14, 49, and 98
Factors of 100 = 1, 2, 4, 5, 10, 20, 25, 50, and 100
Therefore, the common factors of 98 and 200 are 1 and 2.
Example 2: Find the greatest common factor of 98 and 89.
Solution:
Factors of 98 = 1, 2, 7, 14, 49, and 98
Factors of 89 = 1 and 89
So 98 and 89 have only one common factor, that is, 1.
Therefore, the greatest common factor of 98 and 89 is 1.
Example 3: John has 98 marbles and Max has 0 marbles. How many marbles should John give to Max so that both of them have an equal number of marbles?
Solution:
Total number of marbles = 98
The total number of marbles should be distributed equally between John and Max. So, each will get half of the total marbles, that is,
Each of them will get = \(\frac{Total~number~of~marbles}{2}\)
= \(\frac{98}{2}\) [Substitute values]
= \(\frac{49~\times~2}{2}\) [(49,2) is a factor pair of 98]
= 49 [Divide both the numerator and the denominator by 2]
Therefore, John should give 49 marbles to Max.
The factors of 98 are 1, 2, 7, 14, 49, and 98
So, the least factor of 98 is 1, and the greatest factor is 98 itself.
The factors of 98 are 1, 2, 7, 14, 49, and 98
Sum of the factors = 1 + 2 + 7 + 14 + 49 + 98 = 171
So, the sum of the factors of 98 is 171.
Yes, 14 is a factor of 98. This is because when the number 14 divides 98, it leaves 7 as the quotient and 0 as the remainder.
The prime factorization of 98 is 2 × 7 × 7 or 2 × 7\(^2\).
The positive factor pairs of 98 are (1, 98), (2, 49), and (7, 14).