Factors of 98

 

The factors of 98 are 1, 2, 7, 14, 49, and 98 i.e. F₉₈ = {1, 2, 7, 14, 49, 98}. The factors of 98 are all the numbers that can divide 98 without leaving a remainder. 

 

We can check if these numbers are factors of 98 by dividing 98 by each of them. If the result is a whole number, then the number is a factor of 98. Let's do this for each of the numbers listed above:

 

·        1 is a factor of 98 because 98 divided by 1 is 98.

·        2 is a factor of 98 because 98 divided by 2 is 49.

·        7 is a factor of 98 because 98 divided by 7 is 14.

·        14 is a factor of 98 because 98 divided by 14 is 7.

·        49 is a factor of 98 because 98 divided by 49 is 2.

·        98 is a factor of 98 because 98 divided by 98 is 1.

 

 

How to Find Factors of 98?

 

1 and the number itself are the factors of every number. So, 1 and 98 are two factors of 98. To find the other factors of 98, we can start by dividing 98 by the numbers between 1 and 98. If we divide 98 by 2, we get a remainder of 0. Therefore, 2 is a factor of 98. If we divide 98 by 3, we get a remainder of 2. Therefore, 3 is not a factor of 98.

 

Next, we can check if 4 is a factor of 98. If we divide 98 by 4, we get a remainder of 0. Therefore, 4 is also a factor of 98. We can continue this process for all the possible factors of 98.

 

Through this process, we can find that the factors of 98 are 1, 2, 7, 14, 49, and 98. These are the only numbers that can divide 98 without leaving a remainder.

 

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Properties of the Factors of 98

 

The factors of 98 have some interesting properties. One of the properties is that the sum of the factors of 98 is equal to 171. We can see this by adding all the factors of 98 together:

 

1 + 2 + 7 + 14 + 49 + 98 = 171

 

Another property of the factors of 98 is that the prime factors of 98 are 2 and 7.

 

 

Applications of the Factors of 98

 

The factors of 98 have several applications in mathematics. One of the applications is in finding the highest common factor (HCF) of two or more numbers. The HCF is the largest factor that two or more numbers have in common. For example, to find the HCF of 98 and 147, we need to find the factors of both numbers and identify the largest factor they have in common. The factors of 98 are 1, 2, 7, 14, 49, and 98. The factors of 147 are 1, 3, 7, 21, 49, and 147. The largest factor that they have in common is 49. Therefore, the HCF of 98 and 147 is 49.

 

Another application of the factors of 98 is in prime factorization. Prime factorization is the process of expressing a number as the product of its prime factors. The prime factors of 98 are 2, and 7, since these are the only prime numbers that can divide 98 without leaving a remainder. Therefore, we can express 98 as:

 

98 = 2 × 7 × 7

 

We can do prime factorization by division and factor tree method also. Here is the prime factorization of 98 by division method,

 

 

∴ 98 = 2 × 7 × 7

 

Here is the prime factorization of 98 by the factor tree method,

 

 

∴ 98 = 2 × 7 × 7

 

 

Conclusion

 

The factors of 98 are the numbers that can divide 98 without leaving a remainder. The factors of 98 are 1, 2, 7, 14, 49, and 98. The factors of 98 have some interesting properties, such as having a sum of 171. The factors of 98 have several applications in mathematics, such as finding the highest common factor and prime factorization.